Showing papers in "Kyungpook Mathematical Journal in 2010"
TL;DR: In this article, the authors introduce the concept of lacunary statistical and strongly convergence of generalized difference sequence of fuzzy real numbers and prove some inclusion relations and also study some of their properties.
Abstract: In this paper we introduce the concept of lacunary statistical and lacunary strongly convergence of generalized difference sequence of fuzzy real numbers. We prove some inclusion relations and also study some of their properties.
77 citations
TL;DR: In this article, the authors established new inequalities of Ostrowski's type for functions whose derivatives in absolute value are (;m ) convex, and showed that these inequalities can be generalized to functions with convex derivatives.
Abstract: In this paper, we establish new inequalities of Ostrowski's type for functions whose derivatives in absolute value are (;m ) convex.
65 citations
TL;DR: In this paper, a new class of sequence spaces using the concept of n-norm is introduced and investigated for some linear topological structures as well as examine these spaces with respect to derived (n-1)-norm.
Abstract: The main aim of this article is to introduce a new class of sequence spaces using the concept of n-norm and to investigate these spaces for some linear topological structures as well as examine these spaces with respect to derived (n-1)-norm. We use an Orlicz function, a bounded sequence of positive real numbers and some difference operators to construct these spaces so that they become more generalized and some other spaces can be derived under special cases. These investigations will enhance the acceptability of the notion of n-norm by giving a way to construct different sequence spaces with elements in n-normed spaces.
41 citations
TL;DR: In this paper, the authors obtained Fekete-Szego inequality for a normalized analytic function f(z) dened on the open unit disk for which (1 )z(D m ; f (z)) 0 +z (D m+1 ; f(Z)) 0 ( 1 )D m, f(x)+D m +1 ; x) ( 0; m 2 N0; 0) lies in a region starlike with respect to 1.
Abstract: In this present work, the authors obtain Fekete-Szego inequality for certain normalized analytic function f(z) dened on the open unit disk for which (1 )z(D m ; f(z)) 0 +z (D m+1 ; f(z)) 0 (1 )D m ; f(z)+D m+1 ; f(z) ( 0; m 2 N0; 0) lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions dened by Hadamard product (or convolution)
38 citations
TL;DR: In this article, the Hermite-Hadamard integral inequalities for differantiable mappings of real numbers are established. But these inequalities are not applicable to the case of real-valued mappings.
Abstract: In this paper, we establish several new inequalities for some differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.
31 citations
TL;DR: In this paper, the qualitative behavior of the solutions of the difference equation is studied and some qualitative properties of the solution of the problem are discussed. But the qualitative properties are not discussed in detail.
Abstract: In this paper we study some qualitative behavior of the solutions of the difference equation xn+1 = axn + bxn cxn − dxn 1 ; n = 0; 1;:::; where the initial conditions x 1; x0 are arbitrary real numbers and a;b;c;d are positive constants with cx0 − dx 1 0.
27 citations
TL;DR: In this paper, the uniqueness problem of meromorphic functions with differential polynomials was investigated, and a result related to a conjecture of R. Brck and improved the results of I. Lahiri and Q. Zhang was given.
Abstract: In this paper, we investigate the uniqueness problems of meromorphic functions that share a small function with its differential polynomials, and give a result which is related to a conjecture of R. Brck and improve the results of I. Lahiri and Q. C. Zhang.
26 citations
TL;DR: In this paper, the signless Laplacian spectral radius of bicyclic graphs with a given number of pendant vertices was studied and the extremal graph was characterized.
Abstract: In this paper, we study the signless Laplacian spectral radius of bicyclic graphs with given number of pendant vertices and characterize the extremal graphs.
12 citations
TL;DR: In this article, the authors introduce a partitioning subsemimodule of a semimmodule over a semiring which is useful to develop the quotient structure of semimodules.
Abstract: In this paper, we introduce a partitioning subsemimodule of a semimodule over a semiring which is useful to develop the quotient structure of semimodule. Indeed we prove : 1) The quotient semimodule M=N(Q) is essentially independent of choice of Q. 2) If f : M M' is a maximal R-semimodule homomorphism, then . 3) Every partitioning subsemimodule is subtractive. 4) Let N be a Q-subsemimodule of an R-semimodule M. Then A is a subtractive subsemimodule of M with if and only if is a subtractive subsemimodule of .
12 citations
TL;DR: In this paper, a q-extension of the Leibniz rule for q-derivatives via Weyl type qderivative operator is defined. But the main result of this paper is based on the same assumption as in this paper.
Abstract: In the present paper we define a q-extension of the Leibniz rule for q-derivatives via Weyl type q-derivative operator. Expansions and summation formulae for the gener- alized basic hypergeometric functions of one and more variables are deduced as the appli- cations of the main result.
11 citations
Journal Article•
TL;DR: In this article, the qualitative behavior of the solutions of the difference equation with arbitrary real numbers is studied, where the initial conditions x-1, x0 are arbitrary real number and a, b, c, d are positive constants with cx0 - dx-1 ≠ 0.
Abstract: In this paper we study some qualitative behavior of the solutions of the difference equation where the initial conditions x-1, x0 are arbitrary real numbers and a, b, c, d are positive constants with cx0 - dx-1 ≠ 0.
TL;DR: In this article, the generalized Hyers-Ulam stability of the cubic equation f(2x + y) + f (2x y) = 2f(x+y) + 2f[x y] + 12 f(x) in non-Archimedean normed spaces was studied.
Abstract: We give a xed point approach to the generalized Hyers-Ulam stability of the cubic equation f(2x + y) + f(2x y) = 2f(x + y) + 2f(x y) + 12f(x) in non-Archimedean normed spaces. We will give an example to show that some known results in the stability of cubic functional equations in real normed spaces fail in non- Archimedean normed spaces. Finally, some applications of our results in non-Archimedean normed spaces over p-adic numbers will be exhibited.
TL;DR: In this paper, the integral operator is used and a new Hilbert-type integral inequality, whose kernel is the homogeneous form with degree, with three pairs of conjugate exponents and the best constant factor and its reverse form are derived.
Abstract: In this paper, the integral operator is used. We give a new Hilbert-type integral inequality, whose kernel is the homogeneous form with degree - and with three pairs of conjugate exponents and the best constant factor and its reverse form are also derived. It is shown that the results of this paper represent an extension as well as some improvements of the earlier results.
TL;DR: In this paper, the authors established some new and interesting results on the ratio of star-like harmonic univalent functions to their sequences of partial sums, where the analytic part and the co-analytic part of a function are defined separately.
Abstract: . Although, interesting properties on the partial sums of analytic univalentfunctions have been investigated extensively by several researchers, yet analogous resultson partial sums of harmonic univalent functions have not been so far explored. The mainpurpose of the present paper is to establish some new and interesting results on the ratioof starlike harmonic univalent function to its sequences of partial sums. 1. IntroductionA continuous complex-valued function f = u+ ivis said to be harmonic ina simply connected domain D if both uand v are real harmonic in D. In anysimply connected domain we can writef = h+ g, where hand gare analytic inD. We call hthe analytic part and gthe co-analytic part of f:A necessary andsucient condition forf to be locally univalent and sense-preserving in Dis thatjh 0 (z)j>jg(z)j;z2D:See Clunie and Sheil-Small [2].Denote by S H the class of functions f= h+gwhich are harmonic univalent andsense-preserving in the unit disk U= fz: jzj<1gfor which f(0) = f
TL;DR: In this paper, the uniqueness problem of non-constant meromorphic functions in the complex plane was studied and the results of Yang, Yu, Lahiri, and Zhang were improved.
Abstract: . In this paper, we deal with the uniqueness problems of meromorphic functionsthat share a small function with its derivative and improve some results of Yang, Yu, Lahiri,and Zhang, also answer some questions of T. D. Zhang and W. R. Lu.¨ 1. Introduction and main resultsIn this article, by meromorphic functions we shall always mean meromorphicfunctions in the complex plane. we are going to mainly use the basic notationof Nevanlinna Theory, (see [1], [3], [2]) such as T(r,f), N(r,f), m(r,f), N(r,f)and S(r,f) = o(T(r,f)). Let f(z) and g(z) denote two non-constant meromorphicfunctions, and let a(z) be a meromorphic function. If f(z) − a(z) and g(z) − a(z)have the same zeros with the same multiplicities(ignoring multiplicities), then wesay that f(z) and g(z) share a(z) CM(IM). Let k be a positive integer. We denote byN k) (r,1/f−a) the counting function for the zeros of f−a with multiplicity ≤ k, andby N k) (r,1/f −a) the corresponding one for which the multiplicity is not counted.Let N
TL;DR: In this article, the authors investigated curvature-adapted and proper complex equifocal submanifolds in a symmetric space of non-compact type, and showed that the complex Coxeter group associated with a curvatureadapted sub-manifold is the same type group as one associated with the principal orbit of a Hermann type action.
Abstract: In this paper, we investigate curvature-adapted and proper complex equifocal submanifolds in a symmetric space of non-compact type. The class of these submani- folds contains principal orbits of Hermann type actions as homogeneous examples and is included by that of curvature-adapted and isoparametric submanifolds with flat section. First we introduce the notion of a focal point of non-Euclidean type on the ideal bound- ary for a submanifold in a Hadamard manifold and give the equivalent condition for a curvature-adapted and complex equifocal submanifold to be proper complex equifocal in terms of this notion. Next we show that the complex Coxeter group associated with a curvature-adapted and proper complex equifocal submanifold is the same type group as one associated with a principal orbit of a Hermann type action and evaluate from above the number of distinct principal curvatures of the submanifold.
TL;DR: In this article, Chen et al. gave a complete classification of non-degenerate translation surfaces with constant Gauss-Kronecker curvature in R 3, where the curvature is constant.
Abstract: . We study a–ne translation surfaces in R 3 and get a complete classiflcation ofsuch surfaces with constant Gauss-Kronecker curvature. 1. IntroductionA surface in E 3 is called a translation surface if it is obtained as a graph of a func-tion F ( x;y ) = p ( x )+ q ( y ), where p ( x ) and q ( y ) are difierentiable functions. It’s wellknown that a minimal translation surface in the Euclidean space E 3 must be a planeor a Scherk surface, which is the graph of the function F ( x;y ) = ln(cos x= cos y ),the only doubly periodic minimal translation surface.In this note, we study nondegenerate translation surfaces in a–ne space R 3 .This class of surfaces has been studied previously by many geometers. F. Manhart[3] classifled all the nondegenerate a–ne minimal translation surfaces in a–ne spaceR 3 . Further treatments are due to H. F. Sun [5], who classifled the nondegeneratea–ne translation surface with nonzero constant mean curvature in R 3 . Later on,Sun and Chen extended this into the case of hypersurfaces [6]. On the other hand,Binder [1] classifled locally symmetric a–ne translation surfaces in R
TL;DR: In this paper, a weighted geometric mean of positive invertible operators is defined, and a reverse inequality for the arithmetic-geometric mean inequality of the weighted version is shown.
Abstract: A weighted version of the geometric mean of k () positive invertible operators is given. For operators and for nonnegative numbers such that , we define weighted geometric means of two types, the first type by a direct construction through symmetrization procedure, and the second type by an indirect construction through the non-weighted (or uniformly weighted) geometric mean. Both of them reduce to if commute with each other. The first type does not have the property of permutation invariance, but satisfies a weaker one with respect to permutation invariance. The second type has the property of permutation invariance. We also show a reverse inequality for the arithmetic-geometric mean inequality of the weighted version.
TL;DR: In this article, the concepts of 1-prime and 2-prime ideals in semirings were introduced and the m1-system and m2-system in semiring were also introduced.
Abstract: In this paper, we introduce the concepts of 1-prime ideals and 2-prime ideals in semirings. We have also introduced m1-system and m2-system in semiring. We have shown that if Q is an ideal in the semiring R and if M is an m2-system of R such that Q ∩ M = ∅ then there exists as 2-prime ideal P of R such that Q ⊆ P with P ∩ M = ∅:
TL;DR: In this paper, the concepts of fuzzy interior ideals in -rings and semisimple -rings are introduced, and some characterizations of regular -ring are described by means of fuzzy ideals.
Abstract: Some characterizations of regular -rings are described by means of fuzzy ideals. The concepts of fuzzy interior ideals in -rings and semisimple -rings are introduced. Some characterizations of semisimple -rings are investigated by means of fuzzy interior ideals.
TL;DR: In this paper, an extension of Hardy-Hilbert's integral inequality and the corresponding inequality for series are established by introducing some parameters, and the reverses, some particular results and their equivalent forms are considered.
Abstract: In this paper, by introducing some parameters we establish an extension of Hardy-Hilbert's integral inequality and the corresponding inequality for series. As an ap- plication, the reverses, some particular results and their equivalent forms are considered.
TL;DR: In this article, the uniqueness problems of meromorphic functions sharing a small function with their differential polynomials were investigated, and some results related to a conjecture of R. Bruck were obtained.
Abstract: In this paper, we investigate uniqueness problems of meromorphic functions sharing a small function with their differential polynomials, and give some results which are related to a conjecture of R. Bruck, and also improve several previous results.
TL;DR: In this article, the degree of approximation of functions belonging to Lip, Lip((t),r) and W() and classes using (N, )(C, 1) product summability means of its Fourier series is established.
Abstract: A good amount of work has been done on degree of approximation of functions belonging to Lip, Lip((t),r) and W() and classes using Cesro, Nrlund and generalised Nrlund single summability methods by a number of researchers ([1], [10], [8], [6], [7], [2], [3], [4], [9]). But till now, nothing seems to have been done so far to obtain the degree of approximation of functions using (N,)(C, 1) product summability method. Therefore the purpose of present paper is to establish two quite new theorems on degree of approximation of function class and class by (N, )(C, 1) product summability means of its Fourier series.
TL;DR: In this paper, it is shown that an appropriate combination of methods, relevant to opera-tional calculus and to special functions, can be a very useful tool to establish and treat a new class of Hermite and Konhauser polynomials.
Abstract: It is shown that an appropriate combination of methods, relevant to opera- tional calculus and to special functions, can be a very useful tool to establish and treat a new class of Hermite and Konhauser polynomials. We explore the formal properties of the operational identities to derive a number of properties of the new class of Hermite and Konhauser polynomials and discuss the links with various known polynomials.
Abstract: Let A be a locally finite total algebra of finite type such that ai for every operation , elements an and . We show that the weak subalgebra lattice of A uniquely determines its (strong) subalgebra lattice. More precisely, for any algebra B of the same finite type, if the weak subalgebra lattices of A and B are isomorphic, then their subalgebra lattices are also isomorphic. Moreover, B is also total and locally finite.
TL;DR: In this article, the authors introduced the notion of a screen slant light-like submanifold of an indefinite Kenmotsu manifold and provided characterization theorem for the existence of such a sub-manifolds.
Abstract: In this paper, we introduce the notion of a screen slant lightlike submanifold of an indefinite Kenmotsu manifold. We provide characterization theorem for existence of screen slant lightlike submanifold with examples. Also, we give an example of a minimal screen slant lightlike submanifold of and prove some characterization theorems.
TL;DR: In this paper, a new Hilbert-type integral inequality with a best constant factor and a combination kernel involving two mean values is given, which is an extension of Hilbert's integral inequality.
Abstract: By introducing some parameters and using the way of weight function and the technic of real analysis and complex analysis, a new Hilbert-type integral inequality with a best constant factor and a combination kernel involving two mean values is given, which is an extension of Hilbert's integral inequality. As applications, the equivalent form and the reverse forms are considered.
TL;DR: In this paper, a new class of univalent holomorphic functions with fixed finitely many co-efficients based on Generalized fractional derivative was introduced and some important properties of this class such as coefficient bounds, convex combination, extreme points, Radii of starlikeness and convexity were investigated.
Abstract: A new class of univalent holomorphic functions with fixed finitely many co- efficients based on Generalized fractional derivative are introduced. Also some important properties of this class such as coefficient bounds, convex combination, extreme points, Radii of starlikeness and convexity are investigated.
TL;DR: In this paper, the stability and local Hopf bifurcation for a delayed predator-prey system with Holling II functional response were analyzed for a predator-predator model using the basic theorem on zeros of general transcendental function.
Abstract: We consider a delayed predator-prey system with Holling II functional re- sponse. Firstly, the paper considers the stability and local Hopf bifurcation for a delayed prey-predator model using the basic theorem on zeros of general transcendental function, which was established by Cook etc.. Secondly, special attention is paid to the global ex- istence of periodic solutions bifurcating from Hopf bifurcations. By using a global Hopf bifurcation result due to Wu , we show that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of delay. Finally, several numerical simu- lations supporting the theoretical analysis are given.
TL;DR: In this article, the generalized Hyers-Ulam stability of the functional equation f(x + y,z - w) + f (x - y, z + w) = 2f(x, z) + 2f (y, w).
Abstract: By using an idea of Cdariu and Radu [4], we prove the generalized Hyers-Ulam stability of the functional equation f(x + y,z - w) + f(x - y,z + w) = 2f(x, z) + 2f(y, w). The quadratic form given by f(x, y) = is a solution of the above functional equation.