Showing papers in "Filomat in 2017"
TL;DR: In this article, the development of a new five-stages symmetric two-step method of algebraic order with vanished phase-lag and its first, second, third and fourth derivatives is analyzed.
Abstract: The development of a new five-stages symmetric two-step method of fourteenth
algebraic order with vanished phase-lag and its first, second, third and
fourth derivatives is analyzed in this paper. More specifically: (1) we will
present the development of the new method, (2) we will determine the local
truncation error (LTE) of the new proposed method, (3) we will analyze the
local truncation error based on the radial time independent Schrodinger
equation, (4) we will study the stability and the interval of periodicity of
the new proposed method based on a scalar test equation with frequency
different than the frequency of the scalar test equation used for the
phase-lag analysis, (5) we will test the efficiency of the new obtained method
based on its application on the coupled differential equations arising from
the Schrodinger equation.
83 citations
TL;DR: In this article, the authors introduce the concept of a modified $F$-contraction via α-admissible mappings in complete metric spaces, and provide some examples and give an application to an integral equation.
Abstract: In this paper, we introduce the concept of a modified $F$-contraction via $\alpha$-admissible mappings. We initiate study of fixed point theory for such type mappings in complete metric spaces. Moreover, we provide some examples and we give an application to an integral equation.
55 citations
TL;DR: Agarwal et al. as discussed by the authors generalize metrical notions such as completeness, closedness, continuity, g-continuity and compatibility to relation-theoretic setting and utilize these relatively weaker notions to prove results on the existence and uniqueness of coincidence points involving a pair of mappings defined on a metric space endowed with an arbitrary binary relation.
Abstract: In this article, we generalize some frequently used metrical notions such as: completeness, closedness, continuity, g-continuity and compatibility to relation-theoretic setting and utilize these relatively weaker notions to prove results on the existence and uniqueness of coincidence points involving a pair of mappings defined on a metric space endowed with an arbitrary binary relation. Particularly, under universal relation our results deduce the classical coincidence point theorems of Goebel (Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys. 16 (1968) 733-735) and Jungck (Int. J. Math. Math. Sci. 9 (4) (1986) 771-779). In process our results generalize, extend, modify and unify several well-known results especially those obtained in Alam and Imdad (J. Fixed Point Theory Appl. 17 (4) (2015) 693-702), Karapinar et al: (Fixed Point Theory Appl. 2014:92 (2014) 16 pp), Alam et al: (Fixed Point Theory Appl. 2014:216 (2014) 30 pp), Alam and Imdad (Fixed Point Theory, in press) and Berzig (J. Fixed Point Theory Appl. 12 (1-2) (2012) 221-238.
55 citations
TL;DR: In this article, the Gronwall type inequality for generalized normalized fractional operators was obtained for generalized Riemann-Liouville and Hadamard fractional inequalities and applied to the dependence of the solution of differential equations on both the order and the initial conditions.
Abstract: In this paper, we obtain the Gronwall type inequality for generalized
fractional operators unifying Riemann-Liouville and Hadamard fractional
operators. We apply this inequality to the dependence of the solution of
differential equations, involving generalized fractional derivatives, on both
the order and the initial conditions. More properties for the generalized
fractional operators are formulated and the solutions of initial value
problems in certain new weighted spaces of functions are established as
well.
53 citations
TL;DR: The main purpose of as discussed by the authors is to introduce and investigate the concepts of lacunary strong summability of order and statistical convergence of order of real-valued functions which are measurable (in the Lebesgue sense) in the interval (1,∞).
Abstract: The main purpose of this paper is to introduce and investigate the concepts of lacunary strong summability of order and lacunary statistical convergence of order of real-valued functions which are measurable (in the Lebesgue sense) in the interval (1,∞). Some relations between lacunary statistical convergence of order and lacunary strong summability of order are also given.
50 citations
49 citations
TL;DR: In this paper, a theory of separation axioms in the category of stratified L-generalized convergence spaces in the spirit of Lowen is developed. But it does not generalize the theory of Jäger.
Abstract: By using the residual implication on a frame L, we develop a theory of separation axioms in the category of stratified L-generalized convergence spaces in the spirit of Lowen, i.e., we define for each space some degrees of fulfilling T0, T1, T2 and regularity axioms from a logical aspect. These degrees of separation axioms generalize the theory of separation axioms in the sense of Jäger.
49 citations
TL;DR: In this paper, some new inequalities of Simpson-type are established for the classes of functions whose derivatives of absolute values are convex functions via Riemann-Liouville integrals.
Abstract: In this paper some new inequalities of Simpson-type are established for the classes of functions whose derivatives of absolute values are convex functions via Riemann-Liouville integrals. Also, by special selections of n;we give some reduced results.
42 citations
TL;DR: In this paper, the authors introduce the notion of strongly generalized convex functions which are called as strongly η-convex functions and derive integral inequalities of the HermiteHadamard and Hermite Hadamard-Fejér type.
Abstract: The main objective of this article is to introduce the notion of strongly generalized convex functions which is called as strongly η-convex functions. Some related integral inequalities of HermiteHadamard and Hermite-Hadamard-Fejér type are also obtained. Special cases are also investigated.
40 citations
31 citations
TL;DR: In this article, the authors define a proper ideal I of R as an n-ideal if whenever ab ∈ I with a < √ 0, then b∈ I for every a, b ∈ R.
Abstract: In this paper, we present a new classes of ideals: called n-ideal. Let R be a commutative ring with nonzero identity. We define a proper ideal I of R as an n-ideal if whenever ab ∈ I with a < √ 0, then b ∈ I for every a, b ∈ R. We investigate some properties of n-ideals analogous with prime ideals. Also, we give many examples with regard to n-ideals.
TL;DR: In this article, the Wijsman I-lacunary statistical convergence of order α was introduced, and the concept of Wijsmansman strongly I-LACUNARY statistical convergence α was investigated.
Abstract: The idea of I-convergence of real sequences was introduced by Kostyrko et
al. [Kostyrko, P. ; Salat, T. and Wilczynski, W. I-convergence, Real
Anal. Exchange 26(2) (2000/2001), 669-686] and also independently by Nuray
and Ruckle [Nuray, F. and Ruckle,W. H. Generalized statistical convergence
and convergence free spaces, J. Math. Anal. Appl. 245(2) (2000), 513-527].
In this paper we introduce the concepts of Wijsman I-lacunary statistical
convergence of order α and Wijsman strongly I-lacunary statistical
convergence of order α, and investigated between their relationship.
TL;DR: In this paper, the authors employ the fixed point theorems such as Darbo's theorem in Banach algebra concerning the estimate on the solutions of nonlinear functional-integral equations.
Abstract: In the present paper, utilizing the techniques of suitable measures of noncompactness in Banach algebra, we prove an existence theorem for nonlinear functional-integral equation which contains as particular cases several integral and functional-integral equations that appear in many branches of nonlinear analysis and its applications. We employ the fixed point theorems such as Darbo’s theorem in Banach algebra concerning the estimate on the solutions. We also provide a nontrivial example that explain the generalizations and applications of our main result is also included.
TL;DR: An accelerated Jacobi-gradient based iterative (AJGI) algorithm for solving Sylvester matrix equations is presented, which is based on the algorithms proposed by Ding and Chen, Niu et al.[10] and Xie et al[27].
Abstract: In this paper, an accelerated Jacobi-gradient based iterative (AJGI) algorithm for solving Sylvester matrix equations is presented, which is based on the algorithms proposed by Ding and Chen [5], Niu et al.[10] and Xie et al.[27]. Theoretical analysis shows that the new algorithm will converge to the true solution for any initial value under certain assumptions. Finally, several numerical examples are given to verify the efficiency of the accelerated algorithm.
TL;DR: In this article, power inequalities for the Berezin number of a selfadjoint operator in Reproducing Kernel Hilbert Spaces (RKHSs) with applications for convex functions are given.
Abstract: By using Hardy-Hilbert’s inequality, some power inequalities for the Berezin number of a selfadjoint operators in Reproducing Kernel Hilbert Spaces (RKHSs) with applications for convex functions are given.
TL;DR: The definition of the DMP inverse of a square matrix with complex elements was extended to rectangular matrices in this paper, where it was shown that for any A and W, m by n and n by m, respectively, there exists a unique matrix X, such that XAX = X, XA = Wad, wWA and (WA)k+1X =(WA + 1A+1A+, where Ad,w denotes the W-weighted Drazin inverse of A and k = Ind(AW), the index of AW.
Abstract: The definition of the DMP inverse of a square matrix with complex elements is
extended to rectangular matrices by showing that for any A and W, m by n and
n by m, respectively, there exists a unique matrix X, such that XAX = X, XA
= Wad, wWA and (WA)k+1X =(WA)k+1A+, where Ad,w denotes the W-weighted Drazin
inverse of A and k = Ind(AW), the index of AW.
TL;DR: In this paper, the classes of ideal convergent sequences using a new generalized difference matrix and Orlicz functions are introduced, and the different algebraic and topological properties of these classes of sequences are investigated.
Abstract: An ideal $I$ is a family of subsets of positive integers $\mathbb{N}$ which is closed under taking finite unions and subsets of its elements. A sequence $u=(u_k)$ of real numbers is said to be $B^{n}_{(m)}$-ideal convergent to a real number $\ell$ for every $\varepsilon>0,$ the set $$\left\{k\in\mathbb{N}: |B^{n}_{(m)} u_k - \ell|\geq \varepsilon\right\}$$ belongs to $I,$ where $n,m\in\mathbb{N}.$ In this article we introduce the classes of ideal convergent sequences using a new generalized difference matrix $B^{n}_{(m)}$ and Orlicz functions and study their basic facts. Also we investigate the different algebraic and topological properties of these classes of sequences.
TL;DR: In this paper, a reduction result for parallel symmetric covariant tensor fields of order two was obtained for the parallel Ricci solitons with regularity and regularity conditions.
Abstract: Torse-forming $\eta $-Ricci solitons are studied in the framework of almost paracontact metric $\eta $-Einstein manifolds. By adding a technical condition, called regularity and concerning with the scalars provided by the two $\eta $-conditions, is obtained a reduction result for the parallel symmetric covariant tensor fields of order two.
TL;DR: In this article, a non-local boundary value spectral problem for an ordinary differential equation in an interval is investigated, where the boundary conditions of this problem are regular but not strengthened regular.
Abstract: We investigate a nonlocal boundary value spectral problem for an ordinary differential equation in an interval. Such problems arise in solving the nonlocal boundary value for partial equations by the Fourier method of variable separation. For example, they arise in solving nonstationary problems of diffusion with boundary conditions of Samarskii-Ionkin type. Or they arise in solving problems with stationary diffusion with opposite flows on a part of the interval. The boundary conditions of this problem are regular but not strengthened regular. The principal difference of this problem is: the system of eigenfunctions is comlplete but not forming a basis. Therefore the direct applying of the Fourier method is impossible. Based on these eigenfunctions there is constructed a special system of functions that already forms the basis. However the obtained system is not already the system of the eigenfunctions of the problem. We demonstrate how this new system of functions can be used for solving a nonlocal boundary value equation on the example of the Laplace equation.
TL;DR: In this article, the authors introduced the double sequence space $R^{qt}(\mathcal{L}_{s})$ as the domain of four dimensional Riesz matrices.
Abstract: Let $0
TL;DR: In this article, the authors established new inequalities of Simpson's type based on s-convexity via fractional integrals, which generalize the results obtained by Sarikaya et al.
Abstract: In this paper, we establish some new inequalities of Simpson's type based on s-convexity via fractional integrals. Our results generalize the results obtained by Sarikaya et al. [1].
TL;DR: In this article, the authors introduced the concept of prime hyperideal height of a hyperring, which is defined as the height of the prime hyper ideal of the hyperring in Noetherian/Artinian hyperrings.
Abstract: Extending the notion of dimension of a hyperring, we introduce the concept of
height of a prime hyperideal of a hyperring, similarly as in ring theory,
and we present some basic properties and relations with the dimension
notion. In the second part of the article we illustrate some results
concerning the height of prime hyperideals in Noetherian/Artinian
hyperrings.
TL;DR: In this paper, the authors extended the concepts of I -limit superior and I-limit inferior to I -statistical limit superior, and studied their properties for sequence of real numbers.
Abstract: In this paper we have extended the concepts of I -limit superior and I -limit inferior to I -statistical limit superior and I -statistical limit inferior and studied some of their properties for sequence of real numbers.
TL;DR: In this paper, the characteristic polynomial of the power graph for dihedral, semi-dihedral, cyclic and dicyclic groups was computed and the spectrum and Laplacian spectrum of these graphs were computed.
Abstract: Let G be a finite group. The power graph P(G) and its main supergraph S(G) are two simple graphs with the same vertex set G. Two elements x, y ∈ G are adjacent in the power graph if and only if one is a power of the other. They are joined in S(G) if and only if o(x)|o(y) or o(y)|o(x). The aim of this paper is to compute the characteristic polynomial of these graph for certain finite groups. As a consequence, the spectrum and Laplacian spectrum of these graphs for dihedral, semi-dihedral, cyclic and dicyclic groups were computed.
TL;DR: In this article, dual identities were used to prove monotonicity results for the (left Riemann) and (right Caputo) fractional difference operators, respectively, using the corresponding delta type properties.
Abstract: Recently, some authors have proved monotonicity results for delta and nabla
fractional differences separately. In this article, we use dual identities
relating delta and nabla fractional difference operators to prove shortly the
monotonicity properties for the (left Riemann) nabla fractional differences
using the corresponding delta type properties. Also, we proved some
monotonicity properties for the Caputo fractional differences. Finally, we
use the Qoperator dual identities to prove monotonicity results for the
right fractional difference operators.
TL;DR: In this paper, the authors investigated the existing non-unique fixed points of certain operators in the context of b-metric spaces, and the main results unify and cover several existing results on the topic in the literature.
Abstract: In this paper, inspired the very interesting results of Ciric [20], we
investigate the existing non-unique fixed points of certain operators in the
context of b-metric spaces. Our main results unify and cover several
existing results on the topic in the literature.
TL;DR: In this paper, the authors introduce the notion of semi-Hyers-Ulam-Rassias stability, which is a type of stability somehow in-between the Hyers Ulam and HUlam Rassias stabilities.
Abstract: We study different kinds of stabilities for a class of very general nonlinear integro-differential equations involving a function which depends on the solutions of the integro-differential equations and on an integral of Volterra type. In particular, we will introduce the notion of semi-Hyers-Ulam-Rassias stability, which is a type of stability somehow in-between the Hyers-Ulam and Hyers-Ulam-Rassias stabilities. This is considered in a framework of appropriate metric spaces in which sufficient conditions are obtained in view to guarantee Hyers-Ulam-Rassias, semi-Hyers-Ulam-Rassias and Hyers-Ulam stabilities for such a class of integro-differential equations. We will consider the different situations of having the integrals defined on finite and infinite intervals. Among the used techniques, we have fixed point arguments and generalizations of the Bielecki metric. Examples of the application of the proposed theory are included.
TL;DR: In this paper, it was shown that if G is a connected graph on n ≥ 6 vertices, then there exists a set of vertices D with D ≤ n/3 and such that V(G) n====== N[D] is an independent set.
Abstract: We prove the following result: If G be a connected graph on n ≥ 6 vertices,
then there exists a set of vertices D with │D│≤ n/3 and such that V(G) n
N[D] is an independent set, where N[D] is the closed neighborhood of D.
Furthermore, the bound is sharp. This seems to be the first result in the
direction of partial domination with constrained structure on the graph
induced by the non-dominated vertices, which we further elaborate in this
paper.
TL;DR: Using the new Caputo-Liouville derivative with fractional order, the authors modified the nonlinear Schrdinger equation and used an iterative approach to derive an approximate solution of the modified equation.
Abstract: Using the new Caputo-Liouville derivative with fractional order, we have
modified the nonlinear Schrdinger equation. We have shown some useful in
connection of the new derivative with fractional order. We used an iterative
approach to derive an approximate solution of the modified equation. We have
established the stability of the iteration scheme using the fixed point
theorem. We have in addition presented in detail the uniqueness of the
special solution.