Showing papers in "Kyungpook Mathematical Journal in 2016"
Abstract: In this paper, deferred statistical convergence is defined by using deferred Cesàro mean instead of Cesàro mean in the definition of statistical convergence. The obtained method is compared with strong deferred Cesàro mean and statistical convergence under some certain assumptions. Also, some inclusion theorems and examples are given.
46 citations
TL;DR: In this paper, the Riemann-Liouville fractional integrals were used to establish several new inequalities for some difierantiable mappings that are connected with the celebrated Ostrowski type integral inequality.
Abstract: In this paper, we use the Riemann-Liouville fractional integrals to establish several new inequalities for some difierantiable mappings that are connected with the celebrated Ostrowski type integral inequality.
28 citations
19 citations
TL;DR: In this article, the authors gave recursion formulas for three variable Lauricella functions, Srivastava's triple hypergeometric functions, and k-variable Lévy functions.
Abstract: This paper continues the study of recursion formulas of multivariable hypergeometric functions. Earlier, in [4], the authors have given the recursion formulas for three variable Lauricella functions, Srivastava’s triple hypergeometric functions and k–variable Lauricella functions. Further, in [5], we have obtained recursion formulas for the general triple hypergeometric function. We present here the recursion formulas for Exton’s triple hypergeometric functions.
12 citations
TL;DR: The generalized Lucas sequence is considered, then the Binet’s formula is used to show some properties of the (p, q) Lucas number and some generalized identities are obtained.
Abstract: In this paper, we consider the generalized Lucas sequence which is the (p, q) Lucas sequence. Then we used the Binet’s formula to show some properties of the (p, q) Lucas number. We get some generalized identities of the (p, q) Lucas number.
11 citations
10 citations
TL;DR: For complete bipartite graphs, it was shown in this paper that k 0(K`r) = 3 when both r and r are odd, and k 0`r = 4 otherwise.
Abstract: Let H be a graph, and k ≥ χ(H) an integer. We say that H has a cyclic Gray code of k-colourings if and only if it is possible to list all its k-colourings in such a way that consecutive colourings, including the last and the first, agree on all vertices of H except one. The Gray code number of H is the least integer k0(H) such that H has a cyclic Gray code of its k-colourings for all k ≥ k0(H). For complete bipartite graphs, we prove that k0(K`,r) = 3 when both ` and r are odd, and k0(K`,r) = 4 otherwise.
10 citations
TL;DR: In this article, a symbolic algorithm for solving a regular initial value problem (IVP) for a system of linear differential-algebraic equations (DAEs) with constant coefficients has been presented.
Abstract: In this paper, a symbolic algorithm for solving a regular initial value problem (IVP) for a system of linear differential-algebraic equations (DAEs) with constant coefficients has been presented. Algebra of integro-differential operators is employed to express the given system of DAEs. We compute a canonical form of the given system which produces another simple equivalent system. Algorithm includes computing the matrix Green’s operator and the vector Green’s function of a given IVP. Implementation of the proposed algorithm in Maple is also presented with sample computations.
9 citations
TL;DR: In this paper, it was shown that every biharmonic non-degenerate hypersurface in semi-Euclidean space E 5 with constant scalar curvature of diagonal shape operator has zero mean curvature.
Abstract: In this paper, we obtain that every biharmonic non-degenerate hypersurfaces in semi-Euclidean space E 5 with constant scalar curvature of diagonal shape operator has zero mean curvature.
8 citations
TL;DR: In this paper, a notion of ternary distributive algebraic structure is introduced, and a classification of low order structures of this type is given for low-order structures of 3-Lie algebras.
Abstract: We introduce a notion of ternary distributive algebraic structure, give exam- ples, and relate it to the notion of a quandle. Classification is given for low order structures of this type. Constructions of such structures from 3-Lie algebras are provided. We also describe ternary distributive algebraic structures coming from groups and give examples from vector spaces whose bases are elements of a finite ternary distributive set. We intro- duce a cohomology theory that is analogous to Hochschild cohomology and relate it to a formal deformation theory of these structures.
8 citations
TL;DR: In this paper, the uniqueness problem of a meromorphic function sharing one small function with its differential polynomial was investigated, and a result related to a conjecture of R was given.
Abstract: In this paper, we investigate the uniqueness problem of a meromorphic function sharing one small function with its differential polynomial, and give a result which is related to a conjecture of R. .
TL;DR: In this paper, a monotone iteration method for existence as well as approximation of the coupled solutions for a coupled periodic boundary value problem of first order ordinary nonlinear differential equations is proposed.
Abstract: The present paper proposes a new monotone iteration method for existence as well as approximation of the coupled solutions for a coupled periodic boundary value problem of first order ordinary nonlinear differential equations. A new hybrid coupled fixed point theorem involving the Dhage iteration principle is proved in a partially ordered normed linear space and applied to the coupled periodic boundary value problems for proving the main existence and approximation results of this paper. An algorithm for the coupled solutions is developed and it is shown that the sequences of successive approximations defined in a certain way converge monotonically to the coupled solutions of the related differential equations under some suitable mixed hybrid conditions. A numerical example is also indicated to illustrate the abstract theory developed in the paper.
TL;DR: In this paper, the oscillation criteria for the second order nonlinear difierential equation with delay and advanced arguments of the form ((x(t) + a(t),x (t i ae1) + b(t,x( t + ae2)) fi ) 00 + q (t)x fl(t i? 1) + p( t)x ∞ (t +? 2) = 0; t ‚ t0 where fi; fl and ∞ are the ratios of odd positive integers.
Abstract: In this paper we study the oscillation criteria for the second order nonlinear difierential equation with delay and advanced arguments of the form ((x(t) + a(t)x(t i ae1) + b(t)x(t + ae2)) fi ) 00 + q(t)x fl (t i ?1) + p(t)x ∞ (t + ?2) = 0; t ‚ t0 where ae1; ae2; ?1 and ?2 are nonnegative constants and fi; fl and ∞ are the ratios of odd positive integers. Examples are provided to illustrate the main results.
TL;DR: In this paper, the notion of pseudo Q-algebra is introduced, and some properties of their properties are investigated, such as pseudo subalgebra, pseudo ideal, and pseudo atom.
Abstract: As a generalization of Q-algebra, the notion of pseudo Q-algebra is introduced, and some of their properties are investigated. The notions of pseudo subalgebra, pseudo ideal, and pseudo atom in a pseudo Q-algebra are introduced. Characterizations of their properties are provided.
TL;DR: In this paper, the concept of Paraclosed Sets and Paracontinuous Sets were introduced and studied in topological spaces, and the properties of their properties were obtained.
Abstract: In this paper, we introduce and study the concept of a new class of sets called paraopen sets and paraclosed sets in topological spaces. During this process some of their properties are obtained. Also we introduce and investigate a new class of maps called paracontinuous, ∗-paracontinuous, parairresolute, minimal paracontinuous and maximal paracontinuous maps and study their basic properties in topological spaces.
TL;DR: In this paper, the structure of e-local modules and classes of modules via essentially small are investigated, and it is shown that the following conditions are equivalent for a module M : :
Abstract: In this paper, the structure of e-local modules and classes of modules via essentially small are investigated. We show that the following conditions are equivalent for a module M :
TL;DR: In this paper, the authors studied the concircular curvature tensor in a Kenmotsu manifold with respect to the semi-symmetric non-metric connection.
Abstract: The objective of the present paper is to study some new results on concircular curvature tensor in a Kenmotsu manifold with respect to the semi-symmetric non-metric connection.
TL;DR: In this article, the authors provided necessary and sufficient conditions for complete controllability and complete observability of the Sylvester matrix dynamical system with respect to the first order matrix.
Abstract: In this paper, we obtain solution for the first order matrix dynamical system and also we provide set of necessary and sufficient conditions for complete controllability and complete observability of the Sylvester matrix dynamical system.
TL;DR: In this article, the existence and uniqueness of positive solutions for the three-point boundary value problem of nonlinear fractional q-difference equation was investigated, and the results were obtained by applying some standard fixed point theorems.
Abstract: In this paper, we investigate the existence and uniqueness of positive solutions for three-point boundary value problem of nonlinear fractional q-difference equation. Some existence and uniqueness results are obtained by applying some standard fixed point theorems. As applications, two examples are presented to illustrate the main results.
TL;DR: In this paper, the authors extend this result to ∗-prime rings of characteristic different from two and show that at least one of d1, d2 is also a derivation of R.
Abstract: Posner’s first theorem states that if R is a prime ring of characteristic different from two, d1 and d2 are derivations on R such that the iterate d1d2 is also a derivation of R, then at least one of d1, d2 is zero. In the present paper we extend this result to ∗-prime rings of characteristic different from two.
TL;DR: An error embedded Runge-Kutta method that controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method.
Abstract: In this paper, we propose an error embedded Runge-Kutta method to improve the traditional embedded Runge-Kutta method. The proposed scheme can be applied into most explicit embedded Runge-Kutta methods. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. These solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. For the assessment of the effectiveness, the van der Pol equation and another one having a difficulty for the global * Corresponding Author. Received June 28, 2015; accepted October 20, 2015. 2010 Mathematics Subject Classification: 34A45, 65L04, 65L20, 65L70.
TL;DR: In this paper, the authors studied the k-rainbow domatic number in digraphs, and presented some bounds for drk(D) on the maximum number of functions in a krainbow dominating family.
Abstract: For a positive integer k, a k-rainbow dominating function of a digraph D is a function f from the vertex set V (D) to the set of all subsets of the set {1, 2, . . . , k} such that for any vertex v ∈ V (D) with f(v) = ∅ the condition u∈N−(v) f(u) = {1, 2, . . . , k} is fulfilled, where N−(v) is the set of in-neighbors of v. A set {f1, f2, . . . , fd} of k-rainbow dominating functions on D with the property that ∑d i=1 |fi(v)| ≤ k for each v ∈ V (D), is called a k-rainbow dominating family (of functions) on D. The maximum number of functions in a k-rainbow dominating family on D is the k-rainbow domatic number of D, denoted by drk(D). In this paper we initiate the study of the k-rainbow domatic number in digraphs, and we present some bounds for drk(D).
TL;DR: The identities for these polynomials are obtained and the h(x)-B-Tribonacci and h( x-B-Tri Lucas polynmials are introduced.
Abstract: In this paper we introduce h(x)-B-Tribonacci and h(x)-B-Tri Lucas polynomials. We also obtain the identities for these polynomials.
TL;DR: Weakly classical prime submodules were introduced in this paper, where a proper submodule N of an R-module is called a weakly classical submodule if whenever a,b ∈ R and m ∈ M with 0 6 abm ∈ N, then am ∈ n or bm∈ N.
Abstract: In this paper, all rings are commutative with nonzero identity. Let M be an R-module. A proper submodule N of M is called a classical prime submodule, if for each m ∈ M and elements a,b ∈ R, abm ∈ N implies that am ∈ N or bm ∈ N. We introduce the concept of "weakly classical prime submodules". A proper submodule N of M is a weakly classical prime submodule if whenever a,b ∈ R and m ∈ M with 0 6 abm ∈ N, then am ∈ N or bm ∈ N.
TL;DR: In this paper, two kinds variants of the super Catalan matrix as well as their q-analoques are defined and explicit expressions for LU-decompositions of these matrices and their inverses are given.
Abstract: In this paper, we define two kinds variants of the super Catalan matrix as well as their q-analoques. We give explicit expressions for LU-decompositions of these matrices and their inverses.