Showing papers in "Kyungpook Mathematical Journal in 2012"
TL;DR: In this paper, the concepts of lacunary I-convergent sequences are introduced, and different properties of these sequences are investigated, such as solid, symmetric, convergence free etc.
Abstract: In this article we introduce the concepts of lacunary I-convergent sequences. We investigate its different properties like solid, symmetric, convergence free etc.
63 citations
TL;DR: It is proved that the class of I-convergent double sequences of fuzzy real numbers is a complete metric spaces.
Abstract: In this article we introduce the class of I-convergent double sequences of fuzzy real numbers. We have studied different properties like solidness, symmetricity, monotone, sequence algebra etc. We prove that the class of I-convergent double sequences of fuzzy real numbers is a complete metric spaces.
48 citations
TL;DR: In this paper, the Hadamard-type integral inequalities for convex functions were established for ( ;m ) convex function. But these inequalities are not applicable to (m, ε)-convex functions.
Abstract: In this paper we establish several Hadamard-type integral inequalities for ( ;m ) convex functions.
45 citations
TL;DR: In this article, the authors studied properties of commutative BE{algebras and gave the construction of quotient (X =I; ;I) of a commutive BE{ algebra X via an obstinate ideal I of X.
Abstract: In this paper we study properties of commutative BE{algebras and we give the construction of quotient (X=I; ;I) of a commutative BE{algebra X via an obstinate ideal I of X. We construct upper semilattice and prove that is a nearlattice. Finally we dene and study commutative ideals in BE{algebras.
19 citations
TL;DR: In this paper, the authors define a proper ideal of to be 2-absorbing (resp., weakly 2 absorbing) if (resp, ) implies or or, and show that a weakly two absorbing ideal with is 2absorbing.
Abstract: Let be a commutative semiring. We define a proper ideal of to be 2-absorbing (resp., weakly 2-absorbing) if (resp., ) implies or or . We show that a weakly 2-absorbing ideal with is 2-absorbing. We give a number of results concerning 2-absorbing and weakly 2-absorbing ideals and examples of weakly 2-absorbing ideals. Finally we de ne the concept of 0 - (1-, 2-, 3-)2-absorbing ideals of and study the relationship among these classes of ideals of .
17 citations
TL;DR: In this article, necessary and sufficient conditions for a slant curve in a Sasakian 3-manifold to have a C-parallel mean curvature vector were given.
Abstract: In this article, using the example of C. Camci((7)) we reconrm necessary suf- �cient condition for a slant curve. Next, wend some necessary and sufficient conditions for a slant curve in a Sasakian 3-manifold to have: (i) a C-parallel mean curvature vector
12 citations
TL;DR: In this paper, the authors prove some inequalities in terms of G^ateaux derivatives for convex functions dened on linear spaces and also give an improvement of Jensen's inequality, and give applications for norms, mean f-deviations and f-divergence mea- sures.
Abstract: In this paper, we prove some inequalities in terms of G^ateaux derivatives for convex functions dened on linear spaces and also give improvement of Jensen's inequality. Furthermore, we give applications for norms, mean f-deviations and f-divergence mea- sures.
9 citations
TL;DR: In this article, it was shown that the above lemma and its well-known refinement are valid in non-commutative rings, and some interesting consequences are also observed.
Abstract: We show that the above lemma and its well-known refinement are valid, in a general setting, in non-commutative rings. Some interesting consequences are also observed.
9 citations
TL;DR: In this article, the authors introduce the concepts of ordered quasi-ideals, ordered bi-ideal and ordered ternary semigroups and study the properties of these classes.
Abstract: . We introduce the concepts of ordered quasi-ideals, ordered bi-ideals in anordered ternary semigroup and study their properties. Also regular ordered ternarysemigroup is de ned and several ideal-theoretical characterizations of the regular orderedternary semigroups are furnished. 1. IntroductionThe literature of a ternary algebraic system was introduced by D. H. Lehmer[3] in 1932. He investigated certain ternary algebraic systems called triplexes whichturn out to be ternary groups. The notion of ternary semigroup was known toS.Banach. He showed by an example that ternary semigroup does not necessar-ily reduce to an ordinary semigroup. In [6] M. L. Santiago developed the theory ofternary semigroups. He focused his attention mainly to the study of regular ternarysemigroups, bi-ideals and ideals in ternary semigroups. The semigroup Z of all in-tegers under multiplication which plays a vital role in the literature of semigroup.The subset Z + of all positive integers of Z is a semigroup under multiplication.Now if we consider the subset Z of all negative integers of Z, then it is not a semi-group under multiplication. Taking these facts in mind D. H. Lehmer [3] introducedthe notion of ternary semigroup. Z is a natural example of a ternary semigroupunder the ternary multiplication. N. Kehayopulu in [5] developed the theory ofpo-semigroups. He mainly studied regular po-semigroups, ideals and bi-ideals inpo-semigroups. In 1999, Sang Keun Lee and Seong Gon Kang [4] gave charac-
8 citations
TL;DR: In this paper, the authors presented some results on absolute almost generalized Nrlund summability of orthogonal series, and the most important corollaries of the main results were deduced.
Abstract: In this paper we present some results on absolute almost generalized Nrlund summability of orthogonal series. The most important corollaries of the main results also are deduced.
8 citations
TL;DR: Lens surgeries are determined along the Whitehead link by determining necessary conditions to yield a lens space from the Alexander polynomial of the link as: 1, 2 or 3.
Abstract: We determine lens surgeries (i.e. Dehn surgery yielding a lens space) along the n-twisted Whitehead link. To do so, we first give necessary conditions to yield a lens space from the Alexander polynomial of the link as: (1) n = 1 (i.e. the Whitehead link), and (2) one of surgery coefficients is 1, 2 or 3. Our interests are not only lens surgery itself but also how to apply the Alexander polynomial for this kind of problems.
TL;DR: In this paper, the authors characterized polynomials of knots which are transformed into the trefoil knot (and into the gure-eight knot) by a single crossing change.
Abstract: By the works of Kondo and Sakai, it is known that Alexander polynomi- als of knots which are transformed into the trivial knot by a single crossing change are characterized. In this note, we will characterize Alexander polynomials of knots which are transformed into the trefoil knot (and into the gure-eight knot) by a single crossing change.
TL;DR: In this paper, the existence of minimal screen slant light-like submanifolds of an indefinite Sasakian manifold was shown to be true for both screen and radical distributions.
Abstract: In this paper, we introduce screen slant lightlike submanifold of an indefinite Sasakian manifold and give examples. We prove a characterization theorem for the existence of screen slant lightlike submanifolds. We also obtain integrability conditions of both screen and radical distributions, prove characterization theorems on the existence of minimal screen slant lightlike submanifolds and give an example of proper minimal screen slant lightlike submanifolds of .
TL;DR: In this paper, the conditions to characterize projective change between two ( ; )-metrics, such as Matsumoto metric L = 2 and Randers metric � L = � + � on a manifold with dim n > 2, were presented.
Abstract: In the present paper, wend the conditions to characterize projective change between two ( ; )-metrics, such as Matsumoto metric L = 2 and Randers metric � L = � + � on a manifold with dim n > 2, where andare two Riemannian metrics, andare two non-zero 1-forms.
TL;DR: In this article, the authors introduce some new double sequence spaces via ideal convergence and an Orlicz function in -normed spaces and examine some properties of the resulting spaces, including the properties of double-sequence spaces.
Abstract: In this paper we introduce some new double sequence spaces via ideal convergence and an Orlicz function in -normed spaces and examine some properties of the resulting spaces.
TL;DR: In this article, completely irresolute functions and weakly -irresolute function were introduced and their characterizations and their basic properties were obtained. But their properties were not discussed.
Abstract: The purpose of this paper is to introduce two new types of irresolute functions called, completely -irresolute functions and weakly -irresolute functions. We obtain their characterizations and their basic properties.
TL;DR: In this paper, a beautiful formula for rational functions is proved in the square root case, using an interesting link to Chebyshev's polynomials, which allows the determination of the sign of the coefficients of the power series expansion of these rational functions.
Abstract: When Newton's method, or Halley's method is used to approximate the pth root of 1 z, a sequence of rational functions is obtained. In this paper, a beautiful formula for these rational functions is proved in the square root case, using an interesting link to Chebyshev's polynomials. It allows the determination of the sign of the coefficients of the power series expansion of these rational functions. This answers positively the square root case of a proposed conjecture by Guo(2010).
TL;DR: In this paper, a new subclass of multivalent functions with negative coefficients defined by Cho-Kwon-Srivastava operator is introduced, and the coefficient estimate and inclusion relationship involving the neighborhoods of p-valently analytic functions are investigated for this class.
Abstract: In this paper a new subclass of multivalent functions with negative coefficients defined by Cho-Kwon-Srivastava operator is introduced. Coefficient estimate and inclusion relationships involving the neighborhoods of p-valently analytic functions are investigated for this class. Further subordination result and results on partial sums for this class are also found.
TL;DR: In this article, the author proved that all odd cycles, except for the missing case, are Ramsey-innite, and showed that the odd cycles are highly Ramsey-initiate.
Abstract: In a previous paper, the author proved that all odd cycles, except ve cycles, are highly Ramsey-innite. In this paper, we ll in the missing case, and show that ve cycles are highly Ramsey-innite.
TL;DR: In this article, the authors consider a two-dimensional piecewise smooth system which is composed of a linear map and a nonlinear map, and analyze the stability of the system to determine the existence of dangerous border-collision bifurcation.
Abstract: A piecewise smooth system is characterized by non-differentiability on a curve in the phase space. In this paper, we discuss particular bifurcation phenomena in the dy- namics of a piecewise smooth system. We consider a two-dimensional piecewise smooth system which is composed of a linear map and a nonlinear map, and analyze the stability of the system to determine the existence of dangerous border-collision bifurcation. We �nally present some numerical examples of the bifurcation phenomena in the system.
TL;DR: In this article, the Dunwoody polynomial of (1, 1)-knot obtained by the cyclically presented group of the 3-manifold was studied.
Abstract: There is a special connection between the Alexander polynomial of (1, 1)-knot and the certain polynomial associated to the Dunwoody 3-manifold ([3], [10] and [13]). We study the polynomial(called the Dunwoody polynomial) for the (1, 1)-knot obtained by the certain cyclically presented group of the Dunwoody 3-manifold. We prove that the Dunwoody polynomial of (1, 1)-knot in is to be the Alexander polynomial under the certain condition. Then we find an invariant for the certain class of torus knots and all 2-bridge knots by means of the Dunwoody polynomial.
TL;DR: This article reduces the computational cost of the error correction method by making a local approximation of exponential type, which yields an EECM that is exponentially fitted, A-stable and L-stable, independent of the approximation scheme for the error Correction.
Abstract: In this article, we propose exponentially fitted error correction methods(EECM) which originate from the error correction methods recently developed by the authors (see [10, 11] for examples) for solving nonlinear stiff initial value problems. We reduce the computational cost of the error correction method by making a local approximation of exponential type. This exponential local approximation yields an EECM that is exponentially fitted, A-stable and L-stable, independent of the approximation scheme for the error correction. In particular, the classical explicit Runge-Kutta method for the error correction not only saves the computational cost that the error correction method requires but also gives the same convergence order as the error correction method does. Numerical evidence is provided to support the theoretical results.
TL;DR: In this article, a simple explicit type numerical method for discretizations in time for solving one dimensional Burgers' equations is presented, which does not need an iteration process that may be required in most implicit methods and has good convergence and efficiency in computational sense compared to other known numerical methods.
Abstract: In this paper, we present a simple explicit type numerical method for discretizations in time for solving one dimensional Burgers' equations. The proposed method does not need an iteration process that may be required in most implicit methods and have good convergence and efficiency in computational sense compared to other known numerical methods. For evidences, several numerical demonstrations are also provided.
TL;DR: In this paper, a complete classification of four-dimensional pseudo-Riemannian naturally reductive homogeneous spaces is presented, which leads to a complete classification of them.
Abstract: Our attention is turned to four-dimensional pseudo-Riemannian naturally reductive homogeneous spaces. In particular, our study leads to a complete classification of them.
TL;DR: The block LU factorization is used to solve the coupled Stokes equations arisen from an optimal control problem subject to Stokes equation and the convergence of the spectral element solution is proved.
Abstract: The block LU factorization is used to solve the coupled Stokes equations arisen from an optimal control problem subject to Stokes equations. The convergence of the spectral element solution is proved. Some numerical evidences are provided for the model coupled Stokes equations. Moreover, as an application, this algorithm is performed for an optimal control problem.
TL;DR: In this paper, by estimating the weight function, a new Hilbert-type inequality with the integral in the whole plane was given, which is a special case of the result in this paper.
Abstract: In this paper, by estimating the weight function, we give a new Hilbert-type inequality with the integral in whole plane. As its applications, we consider the equivalent and a particular result.
TL;DR: In this paper, it was shown that any graph has a spanning tree T and an alternating sign on T, where the unique path in T joining both end vertices of e has alternatingsigns.
Abstract: . For a spanning tree T of a connected graph Γ and for a labelling φ : E(T) →{+,−}, φ is called an alternating sign on a spanning tree T of a graph Γ if for any cotreeedge e ∈ E(Γ)−E(T), the unique path in T joining both end vertices of e has alternatingsigns. In the present article, we prove that any graph has a spanning tree T and analternating sign on T. 1. IntroductionA graph Γ is an ordered pair Γ = (V (Γ),E(Γ)) comprising a set V(Γ) of verticestogether with a set E(Γ) of edges. A graph is signed if there is a function µ :E(Γ) → {+,−}. A labelling on Γ means to be a 2-edge coloring which is a functionφ : E(Γ) → {+,−} unless stated differently. A graph Γ is bipartite if vertices canbe divided into two disjoint sets S and T such that every edge connects a vertexin S to one in T. A tree is a connected acyclic simple graph. A spanning tree is aspanning subgraph that is a tree. A walk is an alternating sequence of vertices andedges, beginning and ending with a vertex, where each vertex is incident to boththe edge that precedes it and the edge that follows it in the sequence, and where thevertices that precede and follow an edge are the end vertices of that edge. A walkis closed if its first and last vertices are the same, and open if they are different. Apath is an open walk which is simple, meaning that no vertices (and thus no edges)are repeated. We will often omit edges in path if there is no ambiguity.For a spanning tree T of a connected graph Γ, a labeling φ : E(T) → {+,−} iscalled an alternating sign on a spanning tree T of a graph Γ if for any cotree edgee ∈ E(Γ)\E(T), the unique path v
TL;DR: In this paper, the mapping properties of an integral operator are investigated, and it is shown that the function g defined by. belongs to the class if and only if g belongs to g if.
Abstract: The purpose of the present paper is to investigate mapping properties of an integral operator in which we show that the function g defined by . belongs to the class if .
TL;DR: This work deals with soft rings based on some fuzzy sets, in particular, by using the so called 2 soft sets and q-soft sets, which are characterized by special soft sets.
Abstract: We deal with soft rings based on some fuzzy sets, in particular, by using the so called2 soft sets and q-soft sets. Some characterization theorems of soft rings dened on soft sets are given and soft regular rings are hence characterized by special soft sets.
TL;DR: In this article, the authors established evaluation formulas for the analogue of the conditional analytic Fourier-Feynman transform for the function of the form exp {∫ t 0 (s;x(s)) d (s) } (x(t)); x 2 C r (0;t) where is a complex Borel measure on (0,t) and both (s, ) and are the Fourier Stieltjes transforms of the complex BoreL measures on R r.
Abstract: Let C r (0;t) be the function space of the vector-valued continuous paths x : (0;t) ! R r and dene Xt : C r (0;t) ! R (n+1)r and Yt : C r (0;t) ! R nr by Xt(x) = (x(t0);x(t1); ;x(tn 1); x(tn)) and Yt(x) = (x(t0);x(t1); ; x(tn 1)), respec- tively, where 0 = t0 < t1 < < tn = t. In the present paper, using two simple formulas for the conditional expectations overC r (0;t) with the conditioning functionsXt and Yt, we establish evaluation formulas for the analogue of the conditional analytic Fourier-Feynman transform for the function of the form exp {∫ t 0 (s;x(s)) d (s) } (x(t)); x 2 C r (0;t) where is a complex Borel measure on (0;t) and both (s; ) and are the Fourier-Stieltjes transforms of the complex Borel measures on R r .