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

Monotonicity and convexity involving generalized elliptic integral of the first kind

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 $${\mathcal {K}}_a(r)$$ .

Uniqueness of solution for higher-order nonlinear fractional differential equations with multi-point and integral boundary conditions

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.

Sharp power mean bounds for the lemniscate type means

Abstract: In this paper, we present sharp power mean bounds for the so-called lemniscate type means, which were introduced by Neuman (Math Pannon 18(1):77–94, 2007). The obtained results measure what the distance is between the lemniscate-type means and power means. As applications, several new bounds for the arc lemniscate functions are established.

Third Hankel determinant for univalent starlike functions

Abstract: In this paper we obtain the bound of the third Hankel determinant $$\begin{aligned} H_3(1) = \left| \begin{array}{c@{\quad }c@{\quad }c} 1 &{} a_2&{} a_3\\ a_2 &{} a_3&{} a_4\\ a_3 &{} a_4&{} a_5\\ \end{array} \right| \end{aligned}$$ for the class $${\mathcal {S}}^*$$ of univalent starlike functions, i.e. the functions which satisfy in the unit disk the condition $${{\,\mathrm{Re}\,}}\frac{zf'(z)}{f(z)}>0$$ . In our research we apply the correspondence between starlike functions and Schwarz functions and the results obtained by Prokhorov and Szynal and by Carlson.

On the stability, integrability and boundedness analyses of systems of integro-differential equations with time-delay 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.

An accurate and reliable mathematical analytic solution procedure for the EOQ model with non-instantaneous receipt under supplier credits

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.

Some new q-congruences on double 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.

On quantum hybrid fractional conformable differential and integral operators in a complex domain

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.

The use of improved-F expansion method for the time-fractional Benjamin–Ono equation

Abstract: This study investigates new exact solutions of the time-fractional Benjamin–Ono equation by using the improved-F expansion method. Here, the time-fractional derivative is considered in terms of Conformable fractional derivative (CFD). At first, the fractional complex transform is used to convert the time-fractional Benjamin–Ono equation to an ordinary differential equation. Secondly, the proposed method has applied the given equation to construct exact solutions. Finally, all obtained analytical solutions are presented at the end of the paper.

Proof of a generalization of the (C.2) supercongruence of Van Hamme

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.

Logarithmic convexity and increasing property of 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.

A ratio of finitely many gamma functions and its properties with applications

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.

Distinguished $$ C_{p}(X) $$ C p ( X ) spaces

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.

Global and linear convergence of alternated inertial methods for split feasibility problems

Abstract: The focus of this paper is to introduce algorithms with alternated inertial step to solve split feasibility problems. We obtain global convergence of the sequences of iterates generated by the proposed methods under some appropriate conditions. When the split feasibility problem satisfies some bounded linear regularity property, we show that the generated sequences converge linearly. As far as we know, no linear convergence result has been obtained before now for algorithms with inertial steps to solve split feasibility problems in the literature. Our numerical experiments which include a real-world application to jointly constrained Nash equilibrium model show that our methods outperform some inertial methods and other related methods for split feasibility problems in the literature.

Deferred statistical convergence and strongly deferred summable functions

Abstract: In this paper we introduce the concepts of strongly deferred Cesaro summable and $$\mu $$ -deferred statistical convergence of real-valued functions $$x=x(t)$$ which are measurable (in the Lebesgue sense) in the interval $$[1,\infty )$$ . In addition, the relations between the set of strong deferred Cesaro summable and $$\mu $$ -deferred statistical convergent of functions have been examined under some restrictions.

Two new extragradient methods for solving equilibrium problems

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.

Blow-up for a semilinear heat equation with Fujita’s critical exponent on locally finite graphs

Abstract: Let $$G=(V,E)$$ be a locally finite, connected and weighted graph. We prove that, for a graph satisfying curvature dimension condition $$CDE'(n,0)$$ and uniform polynomial volume growth of degree m, all non-negative solutions of the equation $$\partial _tu=\Delta u+u^{1+\alpha }$$ blow up in a finite time, provided that $$\alpha =\frac{2}{m}$$ . We also consider the blow-up problem under certain conditions for volume growth and initial value. These results complement our previous work joined with Lin.

Solvability for two dimensional functional integral equations via Petryshyn’s fixed point theorem

Abstract: This paper aims to use the Petryshyn’s fixed point theorem associated with the measure of non-compactness to prove the existence of solutions of two-dimensional functional integral equations in the Banach algebra of continuous functions on the interval $$ C([0, a]\times [0, \hat{a}],\mathbb {R}), a, \hat{a} > 0.$$ Our existence results contains many functional integral equations as special case that arise in nonlinear analysis. Finally, we present some examples which show that our result is useful for various class of equations.

On the Cusa–Huygens inequality

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}

A new shrinking projection algorithm for a generalized mixed variational-like inequality problem and asymptotically quasi- $$\phi $$ ϕ -nonexpansive mapping in a Banach space

Abstract: We propose and analyze a new inertial type iterative algorithm for finding a common solution of generalized mixed variational-like inequality problem, variational inequality problem for a $$\gamma $$ -inverse strongly monotone mapping and fixed point problem for a asymptotically quasi- $$\phi $$ -nonexpansive mapping in the framework of two-uniformly convex and uniformly smooth real Banach space. Further, we prove that the sequence generated by the proposed iterative algorithm converges strongly to a common solution of these problems. Furthermore, we give some consequences of the main result. Finally, we discuss some numerical examples to demonstrate the applicability of the iterative algorithm. The results presented in this paper unify and extend some known results in this area.

Closed formulas and determinantal expressions for higher-order Bernoulli and Euler polynomials in terms of Stirling numbers

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.

On the behaviors of solutions of systems of non-linear differential equations with multiple constant delays

Abstract: In this paper, non-perturbed and perturbed systems of non-linear differential equations with multiple constant delays are considered. Five new theorems on the qualitative properties of solutions, uniform asymptotic stability (UAS) and instability of trivial solution, boundedness and integrability of solutions, are obtained. The technique of the proofs is based on the construction of two new Lyapunov–Krasovskiĭ functionals (LKFs). An advantage of the new LKFs used here is that they allow to eliminate the Gronwall’s inequality and to obtain more convenient conditions. When we compare our results with the related results in the literature, the established conditions here are new, more convenient and general, less conservative, and they are more suitable for applications. We provide three examples to show the applications of the results of this paper.

Algebraic genericity and summability within the non-Archimedean setting

Abstract: In this paper, we establish the analogue of some recent lineability and algebrability results on the sets of sequences and series within the context of p-adic analysis. More specifically, we prove (among several other results) that: (i) in the space of all p-adic sequences, the set of all convergent sequences for which Cesaro’s Theorem fails is lineable, (ii) the set of all non-absolutely convergent p-adic series considered with Cauchy product or pointwise product is algebrable in $$c_0$$ .

Fractional type multivariate sampling operators

Abstract: In this paper we introduce a novel extension of sampling operators by replacing the sample values $$(f(k/w))_{k=0}^{n}$$ with its fractional average (mean) value in n-dimensional parallelepiped. Using the Riemann–Liouville fractional integral operator of order $$\alpha $$ , we define fractional type multivariate sampling operators based upon a suitable kernel function. Moreover, we give convergence results for these operators in $$C(\mathbf{R}^n)$$ and Orlicz spaces and obtain multivariate Voronovskaya type asymptotic formula by means of Euler-Beta functions. Finally, several graphical and numerical results are presented to demonstrate the accuracy, applicability and efficiency of the operators through special kernels.

Approximations for the complete elliptic integral of the second $$\hbox {Kind}$$ Kind

Abstract: In this paper, we present the best possible parameters $$\alpha _{1}$$ , $$\alpha _{2}$$ , $$\alpha _{3}$$ , $$\alpha _{4}$$ , $$\beta _{1}$$ , $$\beta _{2}$$ , $$\beta _{3}$$ , $$\beta _{4} \in {\mathbb {R}}$$ such that $$\begin{aligned} \frac{\alpha _{1}}{H(x, y)}+\frac{1-\alpha _{1}}{L(x, y)}&<\frac{1}{V(x, y)}<\frac{\beta _{1}}{H(x, y)}+\frac{1-\beta _{1}}{L(x, y)},\\ \frac{\alpha _{2}}{H(x, y)}+\frac{1-\alpha _{2}}{P(x, y)}&<\frac{1}{V(x, y)}<\frac{\beta _{2}}{H(x, y)}+\frac{1-\beta _{2}}{P(x, y)},\\ \frac{\alpha _{3}}{H(x, y)}+\frac{1-\alpha _{3}}{N S(x, y)}&<\frac{1}{V(x, y)}<\frac{\beta _{3}}{H(x, y)}+\frac{1-\beta _{3}}{N S(x, y)},\\ \frac{\alpha _{4}}{H(x, y)}+\frac{1-\alpha _{4}}{T(x, y)}&<\frac{1}{V(x, y)}<\frac{\beta _{4}}{H(x, y)}+\frac{1-\beta _{4}}{T(x, y)} \end{aligned}$$ hold for all $$x, y>0$$ with $$x e y$$ , where H(x, y), G(x, y), L(x, y), A(x, y), NS(x, y), P(x, y) and T(x, y) are respectively the harmonic, geometric, logarithmic, arithmetic, Neuman-Sandor, and first and second Seiffert means of two distinct positive numbers x and y, and $$\begin{aligned} V(x,y)=\pi G^{2}(x, y) /\left[ 2\int _{0}^{\pi /2}\sqrt{A^{2}(x,y) \cos ^{2}\varphi +G^{2}(x,y)\sin ^{2}\varphi }d\varphi \right] \end{aligned}$$ is a new Seiffert-like mean. As applications, some new inequalities for the complete elliptic integral of the second kind are given.

Topological realizations of groups in 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.

A sharp lower bound 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.

$$\frac{1}{2}$$ 1 2 -derivations of Lie algebras and transposed Poisson algebras

Abstract: A relation between $$\frac{1}{2}$$ -derivations of Lie algebras and transposed Poisson algebras has been established. Some non-trivial transposed Poisson algebras with a certain Lie algebra (Witt algebra, the algebra $${\mathcal {W}}(a,-1)$$ , the thin Lie algebra and a solvable Lie algebra with abelian nilpotent radical) have been done. In particular, we have developed an example of the transposed Poisson algebra with associative and Lie parts isomorphic to the Laurent polynomials and the Witt algebra. On the other side, it has been proved that there are no non-trivial transposed Poisson algebras with a Lie algebra part isomorphic to a semisimple finite-dimensional algebra, a simple finite-dimensional superalgebra, the Virasoro algebra, $$N=1$$ and $$N=2$$ superconformal algebras, or a semisimple finite-dimensional n-Lie algebra.

Higher order Lupaş-Kantorovich operators and finite differences

Abstract: It is well-known that Lupas operators are not exponential type operators, although they preserve linear functions. The differential operator is not applicable to estimate nice representation between Lupas operators and its Kantorovich variant. In the present paper we use finite difference method viz. backward differences to estimate the recurrence relation for moments of the Lupas operators. We introduce higher order Lupas-Kantorovich operators and estimate some direct results.

A new approach towards estimating the n-dimensional Bohr radius

Abstract: A new estimate for the Bohr radius of the family of holomorphic functions in the n-dimensional polydisk is provided. This estimate, obtained via a new approach, is sharper than those that are known up to date.