# Showing papers in "Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-matematicas in 2021"

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TL;DR: In this paper, the existence and uniqueness of nonlinear fractional differential equations of higher-order with integral and multi-point boundary conditions are studied. But the authors focus on the problem of self-mappings with contractive iterates in a b-metric-like space.

Abstract: This study is devoted to the development of alternative conditions for existence and uniqueness of nonlinear fractional differential equations of higher-order with integral and multi-point boundary conditions. It uses a novel approach of employing a fixed point theorem based on contractive iterates of the integral operator for the corresponding fixed point problem. We start with developing an existence-uniqueness theorem for self-mappings with contractive iterate in a b-metric-like space. Then, we obtain the unique solvability of the problem under suitable conditions by utilizing an appropriate b-metric-like space.

36 citations

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TL;DR: In this article, the monotonicity properties of the ratio between generalized elliptic integral of the first kind and its approximation for generalized Grotzsch ring function were studied, and the convexity properties of their difference were shown.

Abstract: In this paper, we present the monotonicity properties of the ratio between generalized elliptic integral of the first kind $${\mathcal {K}}_a(r)$$
and its approximation $$\log [1+2/(ar')]$$
, and also the convexity (concavity) of their difference for $$a\in (0,1/2]$$
. As an application, we give new bounds for generalized Grotzsch ring function $$\mu _a(r)$$
and a upper bound for $${\mathcal {K}}_a(r)$$
.

17 citations

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[...]

TL;DR: In this paper, the q-analogue was proved by Gu and Guo, and a new q-congruence modulo and two q-supercongruences modulo were obtained for double basic hypergeometric sums.

Abstract: Swisher confirmed an interesting congruence: for any odd prime p, $$\begin{aligned} \sum _{k=0}^{(p-1)/2}(-1)^k(6k+1)\frac{(\frac{1}{2})_k^{3}}{k!^{3}8^k} \sum _{j=1}^{k}\Bigg (\frac{1}{(2j-1)^{2}}-\frac{1}{16j^{2}}\Bigg ) \equiv 0 \pmod {p}, \end{aligned}$$
which was conjectured by Long. Recently, its q-analogue was proved by Gu and Guo. Inspired by their work, we obtain a new similar q-congruence modulo $$\Phi _n(q)$$
and two q-supercongruences modulo $$\Phi _n(q)^{2}$$
on double basic hypergeometric sums, where $$\Phi _n(q)$$
is the n-th cyclotomic polynomial.

15 citations

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TL;DR: In this article, the q-supercongruence of truncated basic hypergeometric series has been shown to generalize Van Hamme's supercongruences for coprime polynomials by making use of Andrews' multiseries generalization of the Watson transformation and the creative microscoping method.

Abstract: We prove some q-supercongruences for certain truncated basic hypergeometric series by making use of Andrews’ multiseries generalization of the Watson transformation, the creative microscoping method, and the Chinese remainder theorem for coprime polynomials. More precisely, we confirm Conjectures 5.2 and 5.3 in Guo (Adv Appl Math 116:Art. 102016, 2020). As a conclusion, we also prove Conjecture 4.3 in Guo (Integral Transforms Spec Funct 28:888–899, 2017) which may be deemed a generalization of the (C.2) supercongruence of Van Hamme.

14 citations

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[...]

TL;DR: In this article, the authors provide accurate and reliable mathematical analytic solution procedures to improve the findings in the aforementioned work of Huang and Hsu (J Oper Res Soc Jpn 50:1-13, 2007).

Abstract: Recently, Huang and Hsu (J Oper Res Soc Jpn 50:1–13, 2007) investigated the retailer’s optimal replenishment policy with non-instantaneous receipt under trade credit and cash discount. Basically, their inventory model is correct and interesting. However, they ignored explorations of interrelations of functional behaviors of the annual total cost to locate the optimal solutions so much so that the accuracy and reliability of the process of the proof of their solution procedure are questionable. The main purpose of this paper is to provide accurate and reliable mathematical analytic solution procedures to improve the findings in the aforementioned work of Huang and Hsu (J Oper Res Soc Jpn 50:1–13, 2007). Some related recent works on the subject-matter of this investigation are also cited with a view to providing incentive and motivation for making further advances along the lines of the supply chain management and associated inventory problems which we have discussed in this article.

13 citations

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TL;DR: In this article, the authors studied the character of the strongest locally convex topology with respect to a set of vertices of a Corson compact space and showed that a space with strong duals of the strong convex vertices can be distinguished if and only if the vertices are scattered and Eberlein compact.

Abstract: We continue our initial study of $$C_{p}(X) $$
spaces that are distinguished, equiv., are large subspaces of $$\mathbb {R}^{X}$$
, equiv., whose strong duals $$L_{\beta }( X) $$
carry the strongest locally convex topology. Many are distinguished, many are not. All $$L_{\beta }(X) $$
spaces are, as are all metrizable $$C_{p}(X) $$
and $$ C_{k} ( X) $$
spaces. To prove a space $$C_{p}(X) $$
is not distinguished, we typically compare the character of $$L_{\beta }(X) $$
with |X|. A certain covering for X we call a scant cover is used to find distinguished $$C_{p} ( X) $$
spaces. Two of the main results are: (i) $$C_{p}(X) $$
is distinguished if and only if its bidual E coincides with $$\mathbb {R}^{X}$$
, and (ii) for a Corson compact space X, the space $$ C_{p}(X) $$
is distinguished if and only if X is scattered and Eberlein compact.

10 citations

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[...]

TL;DR: In this paper, the Cusa-Huygens inequality was revisited by solving the following problem: given real numbers (a,b, c, b, c) and a real number T ∈ (0,π /2), the necessary and sufficient conditions such that the inequalities hold for the sinc function defined by

Abstract: Sharp bounds of various kinds for the famous unnormalized sinc function defined by $$(\sin x)/x$$
are useful in mathematics, physics and engineering. In this paper, we reconsider the Cusa–Huygens inequality by solving the following problem: given real numbers $$a,b, c\in {{\mathbb {R}}}$$
and $$T\in (0,\pi /2],$$
we find the necessary and sufficient conditions such that the inequalities $$\begin{aligned} \frac{\sin x}{x}>a+b\cos ^{c}x,\quad x\in (0,T) \end{aligned}$$
and $$\begin{aligned} \frac{\sin x}{x}

9 citations

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[...]

TL;DR: In this paper, the author presents several closed forms and determinantal expressions involving Stirling numbers of the second kind for higher-order Bernoulli and Euler polynomials by applying the Faa di Bruno formula and some properties of Bell polynomial.

Abstract: In this paper, the author presents several closed forms and determinantal expressions involving Stirling numbers of the second kind for higher-order Bernoulli and Euler polynomials by applying the Faa di Bruno formula and some properties of Bell polynomials.

7 citations

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[...]

TL;DR: In this paper, the authors established an inequality involving exponential functions and sums, introduced a ratio of finitely many gamma functions, discussed properties, including monotonicity, logarithmic convexity, (logarithmically) complete monotonivity, and the Bernstein function property, of the newly introduced ratio, and constructed two inequalities of multinomial coefficients and multivariate beta functions.

Abstract: In the paper, the authors establish an inequality involving exponential functions and sums, introduce a ratio of finitely many gamma functions, discuss properties, including monotonicity, logarithmic convexity, (logarithmically) complete monotonicity, and the Bernstein function property, of the newly introduced ratio, and construct two inequalities of multinomial coefficients and multivariate beta functions.

6 citations

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TL;DR: In this article, the authors presented new inequalities about hyperbolic functions with much better approximation effect, and provided two-sided bounds of $$(sinh (x)/x)^p.

Abstract: In this paper, we present new inequalities about hyperbolic functions with much better approximation effect. It firstly provides two-sided bounds of $$(\sinh (x)/x)^p$$
for the case $$p \in (0,1]$$
, and lower bound for the case $$p \ge \frac{7}{5}$$
as well. It also provides inequalities about mixed hyperbolic functions consisting of $$\tanh (x)$$
and $$\sinh (x)$$
. Numerical examples show that the new inequalities can achieve much better approximation effect than those of prevailing methods.

5 citations

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[...]

TL;DR: In this paper, a Lyapunov-Krasovskii functional (LKF) was constructed for a linear system of integro-delay differential equations (IDDEs) with constant time retardation.

Abstract: In the paper, Tian and Wang (Appl Math Lett 105:106325, 8 pp, 2020, Theorem 1) took into consideration a linear system of integro-delay differential equations (IDDEs) with constant time retardation. In Tian and Wang (2020), the authors proved a new and interesting theorem concerning asymptotically stability of zero solution of that linear system of IDDEs with constant time retardation. Tian and Wang (2020) constructed a new Lyapunov–Krasovskiĭ functional (LKF) and used that LKF to prove the related theorem on the asymptotically stability. To the best of the information, we would like to note that the asymptotically stability result of Tian and Wang (2020, Theorem 1) consists of very interesting and strong conditions. However, in this paper, we construct a more suitable LKF, then we obtain the result of Tian and Wang (2020, Theorem 1) for uniformly asymptotically stability of zero solution under very weaker condition using that LKF as well as we investigate the integrability of the norm and boundedness of solutions. For illustrative aims, in particular cases, two numerical examples are provided for the uniformly asymptotically stability of zero solution as well as integrability and boundedness of solutions. By this work, we do a contribution to the topic of the paper and relevant literature. The results of this paper have also new contributions to the former literature and they may useful for researchers working on the topics of this paper.

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TL;DR: In this article, the authors extended the hybrid fractional differential operator (HFDO) to the complex domain by using the quantum calculus and derived the q-integral operator corresponding to q-HFDO.

Abstract: Newly, the hybrid fractional differential operator (HFDO) is presented and studied in Baleanu et al. (Mathematics 8.3:360, 2020). This work deals with the extension of HFDO to the complex domain and its generalization by using the quantum calculus. The outcome of the above conclusion is a q-HFDO, which will employ to introduce some classes of normalized analytic functions containing the well-known starlike and convex classes. Moreover, we utilize the quantum calculus to formulate the q-integral operator corresponding to q-HFDO. As a result, the upper solution is exemplified by utilizing the notion of subordination inequality.

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TL;DR: In this article, the authors define a hyperbolic extension of a paraholomorphic paracomplex Riemannian manifold and show that it is a para-Sasaki-like manifold.

Abstract: We determine a new class of paracontact paracomplex Riemannian manifolds derived from certain cone construction, called para-Sasaki-like Riemannian manifolds, and give explicit examples. We define a hyperbolic extension of a paraholomorphic paracomplex Riemannian manifold, which is a local product of two Riemannian spaces of equal dimension, and show that it is a para-Sasaki-like Riemannian manifold. If the original paraholomorphic paracomplex Riemannian manifold is a complete Einstein space of negative scalar curvature, then its hyperbolic extension is a complete Einstein para-Sasaki-like Riemannian manifold of negative scalar curvature. Thus, we present new examples of complete Einstein Riemannian manifolds of negative scalar curvature.

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TL;DR: In this paper, two new extragradient variants for the classical equilibrium problem in real Hilbert spaces are introduced. But their convergence assumptions are weaker than those assumed in related works in the literature.

Abstract: In this paper, we are concern with the classical equilibrium problem in real Hilbert spaces and introduce two new extragradient variants for it. By taking into account several fixed point theory techniques, we obtain simple structure methods that converge strongly and hence demonstrate the theoretical advantage of our methods. Moreover, our convergence assumptions are weaker than those assumed in related works in the literature. Primary numerical examples with comparisons illustrate the behaviour of our proposed scheme and show its advantages.

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University of Johannesburg

^{1}, VIT University^{2}, Ton Duc Thang University^{3}, Indiana University^{4}TL;DR: In this paper, the authors studied unified Feng-Liu type fixed point theorems using $$(\alpha,\eta )-muti-valued admissible mappings with more general contraction condition in complete metric spaces.

Abstract: The propose of this work is to study unified Feng-Liu type fixed point theorems using $$(\alpha ,\eta )$$
-muti-valued admissible mappings with more general contraction condition in complete metric spaces. The obtained results generalize and improve several existing theorems in the literature. We use these results in metric spaces endowed with binary relations and partially ordered sets. Some non-trivial example have been presented to illustrate facts and show genuineness of our work. At the end, the established results will be used to obtain existence solutions for a fractional-type integral inclusion.

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TL;DR: In this article, the authors provide new refinements of Becker-Stark inequality and Cusa-Huygens inequality using trigonometric polynomial method, which is useful for establishing new inequalities and refining some existing inequalities.

Abstract: The aim of this paper is to provide new refinements of Becker-Stark inequality and Cusa-Huygens inequality using trigonometric polynomial method. It is shown that the approach proposed is useful for establishing new inequalities and refining some existing inequalities.

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TL;DR: In this article, a 4-convex and green function was proposed to improve Jensen's type inequalities via 4-Convolutional and Green functions, which can be used to obtain new bounds for the Hermite-Hadamard gap.

Abstract: In this article, we present some new improvements of Jensen’s type inequalities via 4-convex and Green functions. These improvements are demonstrated in discrete as well as in integral versions. The aforesaid results enable us to give some improvements of Jensen’s and the Jensen–Steffensen inequalities. Also, we present some improvements of the reverse Jensen’s and the Jensen–Steffensen inequalities. Then as consequences of the improved Jensen’s inequality, we deduce some new bounds for the power, geometric and quasi-arithmetic means, also obtain bounds for the Hermite–Hadamard gap and improvements of the Holder inequality. Finally as applications of the improved Jensen’s inequality, we present some new bounds for various divergences and Zipf–Mandelbrot entropy.

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TL;DR: In this article, the authors studied colored triangulations of compact simply-connected PL 4-manifolds with empty or connected boundary which induce handle decompositions lacking in 1-handles or in 1 and 3-handels.

Abstract: In this paper we study colored triangulations of compact PL 4-manifolds with empty or connected boundary which induce handle decompositions lacking in 1-handles or in 1- and 3-handles, thus facing also the problem, posed by Kirby, of the existence of special handle decompositions for any simply-connected closed PL 4-manifold. In particular, we detect a class of compact simply-connected PL 4-manifolds with empty or connected boundary, which admit such decompositions and, therefore, can be represented by (undotted) framed links. Moreover, this class includes any compact simply-connected PL 4-manifold with empty or connected boundary having colored triangulations that minimize the combinatorially defined PL invariants regular genus, gem-complexity or G-degree among all such manifolds with the same second Betti number.

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TL;DR: In this paper, with the aid of the Cebysev integral inequality, by virtue of the integral representation of the Riemann zeta function, with the use of two properties of a function and its derivatives involving the exponential function and the Stirling numbers of the second kind, by means of complete monotonicity, the authors established logarithmic convexity and increasing property of four sequences involving the Bernoulli numbers and their ratios.

Abstract: In the paper, with the aid of the Cebysev integral inequality, by virtue of the integral representation of the Riemann zeta function, with the use of two properties of a function and its derivatives involving the exponential function and the Stirling numbers of the second kind, by means of complete monotonicity, the authors establish logarithmic convexity and increasing property of four sequences involving the Bernoulli numbers and their ratios.

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TL;DR: In this paper, it was shown that every group can be realized as the homeomorphism group and as the group of homotopy classes of (pointed) self-homotopy equivalences of infinitely many non-homomorphism-equivalent Alexandroff spaces.

Abstract: We prove that every group can be realized as the homeomorphism group and as the group of (pointed) homotopy classes of (pointed) self-homotopy equivalences of infinitely many non-homotopy-equivalent Alexandroff spaces.

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TL;DR: The authors showed that the inequality holds for the Gaussian arithmetic-geometric mean in terms of logarithmic and arithmetic means with the best constants for the complete elliptic integrals of the first kind.

Abstract: Let $${\mathcal {K}}\left( r\right) $$
be the complete elliptic integrals of the first kind and $$\text{ arth }r$$
denote the inverse hyperbolic tangent function. We prove that the inequality $$\begin{aligned} \frac{2}{\pi }{\mathcal {K}}\left( r\right) >\left[ 1-\lambda +\lambda \left( \frac{\text{ arth }r}{r}\right) ^{q}\right] ^{1/q} \end{aligned}$$
holds for $$r\in \left( 0,1\right) $$
with the best constants $$\lambda =3/4$$
and $$q=1/10$$
. This improves some known results and gives a positive answer for a conjecture on the best upper bound for the Gaussian arithmetic–geometric mean in terms of logarithmic and arithmetic means.

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TL;DR: In this article, the twisted Alexander polynomials of the affine complement M of a complex essential hyperplane arrangement were investigated, as well as those of punctured stratified tubular neighborhoods of complex essential line arrangements.

Abstract: We study torsion properties of the twisted Alexander modules of the affine complement M of a complex essential hyperplane arrangement, as well as those of punctured stratified tubular neighborhoods of complex essential hyperplane arrangements. We investigate divisibility properties between the twisted Alexander polynomials of the two spaces, compute the (first) twisted Alexander polynomial of a punctured stratified tubular neighborhood of an essential line arrangement, and study the possible roots of the twisted Alexander polynomials of both the complement and the punctured stratified tubular neighborhood of an essential hyperplane arrangement in higher dimensions. We apply our results to distinguish non-homeomorphic homotopy equivalent arrangement complements. We also relate the twisted Alexander polynomials of M with the corresponding twisted homology jump loci.

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TL;DR: In this paper, generalized hypergeometric Bernoulli numbers for Dirichlet characters were introduced and properties, including relations, expressions and determinants, of these numbers were studied.

Abstract: We introduce generalized hypergeometric Bernoulli numbers for Dirichlet characters We study their properties, including relations, expressions and determinants At the end in Appendix we derive first few expressions of these numbers

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TL;DR: In this paper, a Lyapunov-type and a Hartman-Wintner-type inequality were obtained for a nonlinear fractional hybrid equation with left Riemann-Liouville and right Caputo fractional derivatives of order = 1/2 < α 1/1/2 subject to Dirichlet boundary conditions.

Abstract: In this paper, we obtain a Lyapunov-type and a Hartman–Wintner-type inequalities for a nonlinear fractional hybrid equation with left Riemann–Liouville and right Caputo fractional derivatives of order $$1/2<\alpha \le 1,$$
subject to Dirichlet boundary conditions. It is also shown that failure of the Lyapunov-type and Hartman–Wintner-type inequalities, corresponding nonlinear boundary value problem has only trivial solutions. In the case $$\alpha =1$$
, our results coincide with the classical Lyapunov and Hartman–Wintner inequalities, respectively.

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TL;DR: In this paper, the sine and hyperbolic tangent means in terms of various weighted means of the arithmetic and centroidal means were studied and the optimal bounds for the tangent mean of the SINR were provided.

Abstract: We provide optimal bounds for the sine and hyperbolic tangent means in terms of various weighted means of the arithmetic and centroidal means

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TL;DR: In this article, the authors provide a complete characterization of the possible sets of periods for Devaney chaotic linear operators on Hilbert spaces and derive a characterization for linearizable maps on Banach spaces.

Abstract: We provide a complete characterization of the possible sets of periods for Devaney chaotic linear operators on Hilbert spaces. As a consequence, we also derive this characterization for linearizable maps on Banach spaces.

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TL;DR: In this paper, the authors introduced the concepts of Lebesgue-Stieltjes (LSTJ) and combined theory on time scales, and established the relationships, the extensions and the composition theorems.

Abstract: In this paper, we introduce the concepts of Lebesgue–Stieltjes $$\Diamond _\alpha $$
-measure, $$\Diamond _\alpha $$
-measurable function and $$\Diamond _\alpha $$
-integral. Based on the theory of combined measurability on time scales, some basic properties including the relationships, the extensions and the composition theorems are established. Particularly, through the switch coefficient of combined theory on time scales, one can obtain the Lebesgue–Stieltjes $$\varDelta $$
-measure and Lebesgue–Stieltjes $$
abla $$
-measure if by taking $$\alpha =1$$
and $$\alpha =0$$
, respectively. In addition, several examples are provided to demonstrate the effectiveness of the obtained results in each section.

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TL;DR: In this paper, the classical form of the Ebola virus disease model has been modified by using new fractional derivatives and the resulting fractional forms of the EBV disease model have then been examined by applying a newly developed semi-analytical method.

Abstract: Ebola virus disease is a fatal hemorrhagic fever of humans and primates caused by viruses. There are many mathematical models to investigate this viral disease. In this paper, the classical form of the Ebola virus disease model has been modified by using new fractional derivatives. The resulting fractional forms of the Ebola virus disease model have then been examined by applying a newly-developed semi-analytical method. The optimal perturbation iteration method has been implemented to obtain new approximate solutions to the system of differential equations which better model the Ebola virus disease. New algorithms are constructed by using three types of operators of fractional derivatives. A real-world problem is also solved in order to prove the efficiency of the proposed algorithms. A good agreement has been found with the real values of the parameters. Finally, several graphical illustrations are presented for different values of the involved biological parameters to show the effects of the new approximate solutions. Obtained results prove that the new method is highly accurate in solving these types of fractional models.

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TL;DR: A survey of divisibility properties of random r-tuples of positive integers can be found in this paper, where the authors present a survey of the rich theory, some of it quite recent.

Abstract: This paper is devoted to survey the rich theory, some of it quite recent, concerning the divisibility properties, of various kinds, of random r-tuples of positive integers.

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TL;DR: In this article, the authors study non-abelian pq-fold regular covers of the projective line, determine algebraic models for some special cases and provide a general isogeny decomposition of the corresponding Jacobian varieties.

Abstract: Let p and q be odd prime numbers. In this paper we study non-abelian pq-fold regular covers of the projective line, determine algebraic models for some special cases and provide a general isogeny decomposition of the corresponding Jacobian varieties. We also give a classification and description of the one-dimensional families of compact Riemann surfaces as before.