Showing papers in "Communications of The Korean Mathematical Society in 2012"
TL;DR: In this paper, Agarwal and O'Regan prove common xed point theorems for g-non-decreasing mappings which sat- isfy some generalized nonlinear contractions in partially ordered complete quasi b-metric spaces.
Abstract: Using the concept of a g-monotone mapping we prove some common xed point theorems for g-non-decreasing mappings which sat- isfy some generalized nonlinear contractions in partially ordered complete quasi b-metric spaces. The new theorems are generalizations of very re- cent xed point theorems due to L. Ciric, N. Cakic, M. Rojovic, and J. S. Ume, (Monotone generalized nonlinear contractions in partailly ordered metric spaces , Fixed Point Theory Appl. (2008), article, ID-131294) and R. P. Agarwal, M. A. El-Gebeily, and D. O'Regan (Generalized contrac- tions in partially ordered metric spaces , Appl. Anal. 87 (2008), 1{8).
43 citations
TL;DR: In this article, the notions of terminal sections of -algebras are introduced and characterizations of a commutative -algebra are provided, where terminal sections are defined as terminal segments of an algebra.
Abstract: The notions of terminal sections of -algebras are introduced. Characterizations of a commutative -algebra are provided.
28 citations
TL;DR: In this paper, Georgescu and Iorgulescu introduced pseudo-BCK-algebras, a subclass of B-algebra with properties similar to those of pseudo BCK.
Abstract: . In this paper we consider pseudo- BCK=BCI -algebras. Inparticular, we consider properties of minimal elements ( x a implies x = a ) in terms of the binary relation which is reexive and anti-symmetric along with several more complicated conditions. Some of theproperties of minimal elements obtained bear resemblance to properties of B -algebras in case the algebraic operations and ◦ are identical, includ-ing the property 0 ◦ (0 a ) = a . The condition 0 (0 ◦x ) = 0 ◦ (0 x ) = x forall x 2 X de nes the class of p -semisimple pseudo- BCK=BCI -algebras(0 x implies x = 0) as an interesting subclass whose further propertiesare also investigated below. 1. IntroductionY. Imai and K. Iseki introduced two classes of abstract algebras: BCK -algebras and BCI -algebras ([6, 7]). We refer useful textbooks for BCK=BCI -algebra to [5, 10, 11]. G. Georgescu and A. Iorgulescu ([3]) introduced thenotion of a pseudo BCK -algebra as an extension of BCK -algebra, and Y. B.Jun([8])characterizedpseudo
14 citations
TL;DR: In this paper, a discrete duality for TSH-algebras with operators with operators was proposed. But this duality was only applied to a propositional calculus.
Abstract: In this article, we continue the study of tense symmetric Heyting algebras (or TSH-algebras). These algebras constitute a generalization of tense algebras. In particular, we describe a discrete duality for TSH-algebras bearing in mind the results indicated by Or lowska and Rewitzky in [E. Or lowska and I. Rewitzky, Discrete Dualities for Heyting Algebras with Operators, Fund. Inform. 81 (2007), no. 1-3, 275–295] for Heyting algebras. In addition, we introduce a propositional calculus and prove this calculus has TSH-algebras as algebraic counterpart. Finally, the duality mentioned above allowed us to show the completeness theorem for this calculus.
13 citations
TL;DR: In this article, the geometry of light-like hypersurfaces M of an inde nite cosymplectic manifold such that either the characterist vector field of M belongs to the screen distribution S(TM) of M or the orthogonal complement of S (TM) in M is studied.
Abstract: We study the geometry of lightlike hypersurfaces M of an inde nite cosymplectic manifold such that either (1) the characterist vector field of belongs to the screen distribution S(TM) of M or (2) belongs to the orthogonal complement of S(TM) in
12 citations
TL;DR: In this article, the authors introduce the notion of (δ, δ′)-continuous functions on generalized topological spaces and investigate characterizations for such functions, and study the relationship between continuity and several types of continuity.
Abstract: We introduce the notion of (δ,δ′)-continuous functions on generalized topological spaces and investigate characterizations for such functions. We study the relationship between (δ,δ′)-continuity and several types of continuity on generalized topological spaces.
12 citations
TL;DR: In this paper, a 3D trans-Sasakian manifold with conservative curvature tensor and 3D conformally flat trans-sakian manifolds are studied.
Abstract: The object of the present paper is to study 3-dimensional trans-Sasakian manifolds with conservative curvature tensor and also 3-dimensional conformally flat trans-Sasakian manifolds. Next we consider compact connected -Einstein 3-dimensional trans-Sasakian manifolds. Finally, an example of a 3-dimensional trans-Sasakian manifold is given, which verifies our results.
11 citations
TL;DR: In this paper, the authors consider quasi-Einstein manifolds satisfying the conditions,,, and where,, and denote the conformal curvature tensor, the quasi-conformal curve tensor and the pseudo projective curve tensors, respectively.
Abstract: We consider -quasi Einstein manifolds satisfying the conditions , , , and where , , and denote the conformal curvature tensor, the quasi-conformal curvature tensor, the projective curvature tensor and the pseudo projective curvature tensor, respectively.
11 citations
TL;DR: In this article, it was shown that if a 3-dimensional non-Sasakian (k, μ)-contact metric manifold satisfies such curvature conditions, then the manifold reduces to an N(k)-contact manifold.
Abstract: In this paper we study h-projectively semisymmetric, φ-projectively semisymmetric, h-Weyl semisymmetric and φ-Weyl semisymmetric non-Sasakian (k, μ)-contact metric manifolds. In all the cases the manifold becomes an η-Einstein manifold. As a consequence of these results we obtain that if a 3-dimensional non-Sasakian (k, μ)-contact metric manifold satisfies such curvature conditions, then the manifold reduces to an N(k)-contact metric manifold.
10 citations
TL;DR: In this article, the authors extend and generalize the results of Altun and Turkoglu [9] in the sense that the concept of occasionally weakly compatible maps is the most general among all the commutativity concepts.
Abstract: In this paper, we prove common fixed point theorems for families of occasionally weakly compatible mappings in Menger spaces using implicit relation Our results extend and generalize the results of Altun and Turkoglu [9] in the sense that the concept of occasionally weakly compatible maps is the most general among all the commutativity concepts Also the completeness of the whole space, continuity of the involved maps and containment of ranges amongst involved maps are completely relaxed
9 citations
TL;DR: In this article, the Euler-Lagrange equation is derived from the theory of biharmonic maps in Rie-mannian geometry, and a smooth map φ : (M,g) → (N,h) between Riemannian manifolds is said to be biminimal if it is a critical point of the bienergy functional.
Abstract: . We study biminimalcurves in 2-dimensional Riemannian man-ifolds of constant curvature. IntroductionElastic curves provide examples of classically known geometric variationalproblem. A plane curve is said to be an elastic curve if it is a critical point ofthe elastic energy, or equivalently a critical point of the total squared curvature[9].In this paper, we study another geometric variational problem of curves inRiemannian 2-manifolds of constant curvature. The Euler-Lagrange equationstudied in this paper is derived from the theory of biharmonic maps in Rie-mannian geometry.A smooth map φ : (M,g) → (N,h) between Riemannian manifolds is saidto be biharmonic if it is a critical point of the bienergy functional:E 2 (φ) =Z M |τ(φ)| 2 dv g ,where τ(φ) = tr ∇dφ is the tension field of φ. Clearly, if φ is harmonic, i.e.,τ(φ) = 0, then φ is biharmonic. A biharmonic map is said to be proper if it isnot harmonic.Chen and Ishikawa [3] studied biharmonic curves and surfaces in semi-Euclidean space (see also [6]). Caddeo, Montaldo and Piu [1] studied bihar-monic curves on Riemannian 2-manifolds. They showed that biharmonic curveson Riemannian 2-manifolds of non-positive curvature are geodesics. Proper bi-harmonic curves on the unit 2-sphere are small circles of radius 1/√2.Next, Loubeau and Montaldo introduced the notion of biminimal immersion[10].An isometric immersion φ : (M,g) → (N,h) is said to be biminimal if it is acritical point of the bienergy functional under all normal variations. Thus thebiminimality is weaker than biharmonicity for isometric immersions, in general.
TL;DR: In this article, the authors established the classical Saalschutz's theorem for the series 3 F 2 (1) by following a method similar to the one presented in this paper.
Abstract: . The aim of this paper is to establish the well-known and veryuseful classical Saalschutz’s theorem for the series 3 F 2 (1) by following afft method. In addition to this, two summation formulas closelyrelated to the Saalschutz’s theorem have also been obtained. The resultsestablished in this paper are further utilized to show how one can obtaincertain known and useful hypergeometric identities for the series 3 F 2 (1)and 4 F 3 (1) already available in the literature. 1. Introduction and results requiredWe start with the following well-known and useful classical Saalschutz’stheorem [4, p. 87, Section 51] for the series 3 F 2 (1). If n is a non-negativeinteger and if a , b , c are independent of n ,(1.1) 3 F 2 [ n; a; bc; 1+ a + b c n ; 1]=( c a ) n ( c b ) n ( c ) n ( c a b ) n : As mentioned in almost all the standard books on generalized hypergeomet-ric series that this theorem can be established with the help of the followingEuler’s transformation formula [4, p. 60, Eq.(5)]. If
TL;DR: In this paper, some new results on the characteriza- tions of the Pareto distribution by upper record values have been estab- lished, and it appears from literature that not much attention has been paid to the characterizations of the pareto distributions.
Abstract: Many researchers have studied the characterizations of prob- ability distributions based on record values. It appears from literature that not much attention has been paid to the characterizations of the Pareto distribution. In this note, some new results on the characteriza- tions of the Pareto distribution by upper record values have been estab- lished.
TL;DR: In this paper, the authors investigated partition congruences for overcubic partition functions and showed a close relation between a certain type of partition function and Ra-manujan's cubic continued fraction.
Abstract: . Inthisnote,weinvestigatepartitioncongruencesforacertaintypeofpartitionfunction,whichisnamedastheovercubicpartitionpairsinlightoftheliterature. Letcp(n)bethenumberofovercubicpartitionpairs. Thenwewillprovethefollowingcongruences:cp(8n+7)≡0 (mod64) and cp(9m+3)≡0 (mod3). 1. IntroductionIn a paper [3], H.-C. Chan initiated the study of the cubic partitions byshowing a close relation between a certain type of partition function and Ra-manujan’s cubic continued fraction. Cubic partition function c(n) is definedbyX ∞n=0 c(n)q n =1(q;q) ∞ (q 2 ;q 2 ) ∞ .Here and in the sequel, we will use the following standard q-series notation:(a;q) ∞ :=Y ∞n=1 (1−aq n−1 ), |q| < 1.Motivated by his works ([3, 4, 5]), many partition congruences for analogouspartition functions have been investigated. In particular, the author studiedits overpartition analog [7] in which the overcubic partition function c(n) wasdefined by(1.1)X ∞n=0 c(n)q n =(−q;q) ∞ (−q 2 ;q 2 ) ∞ (q;q) ∞ (q 2 ;q 2 ) ∞ . ReceivedApril26,2011.2010 Mathematics Subject Classification. 11P83.Key words and phrases. partition,cubicpartition,overcubicpartitionpair.
TL;DR: In this paper, the authors improved the results of Soliman et al. by absorbing pairs of Lipschitzian mappings, as opposed to weak compatibility and the peculiar condition initiated by Pant (15) to ascertain the common xed points.
Abstract: The purpose of this paper is to improve certain results proved in a recent paper of Soliman et al. (20). These results are the outcome of utilizing the idea of absorbing pairs due to Gopal et al. (6) as opposed to two conditions namely: weak compatibility and the peculiar condition initiated by Pant (15) to ascertain the common xed points of Lipschitzian mappings. Some illustrative examples are also furnished to highlight the realized improvements.
TL;DR: In this paper, it was shown that if (, -, +, 0) is a -algebra, then (, +) is an identity semigroup with identity 0.
Abstract: In this note we investigate some properties of -algebras and further relations with -algebras. Especially, we show that if (, -, +, 0) is a -algebra, then (, +) is a semigroup with identity 0. We discuss some constructions of linear -algebras in a field .
TL;DR: In this paper, a fuzzy version of stability for the functional equation in the sense of M. Mirmostafaee and M. S. Moslehian is investigated. But it is not shown that the fuzzy version is optimal.
Abstract: In this paper, we investigate a fuzzy version of stability for the functional equation in the sense of M. Mirmostafaee and M. S. Moslehian.
TL;DR: In particular, Chen and Chang as mentioned in this paper proved common fixed point theorems for single-valued and set-valued occasionally weakly compatible mappings in Menger spaces, and extended these results.
Abstract: In the present paper, we prove common fixed point theorems for single-valued and set-valued occasionally weakly compatible mappings in Menger spaces. Our results improve and extend the results of Chen and Chang (Chi-Ming Chen and Tong-Huei Chang, Common fixed point theorems in Menger spaces, Int. J. Math. Math. Sci. 2006 (2006), Article ID 75931, Pages 1-15).
TL;DR: In this paper, the notion of an enlarged p-ideal and a fuzzy pideal in BCI-algebras with degree is introduced and related properties of them are investigated.
Abstract: . The notion of an enlarged p-ideal and a fuzzy p-ideal in BCI-algebras with degree are introduced. Related properties of them are in-vestigated. 1. IntroductionThe concept of a fuzzy set is applied to generalize some of the basic conceptsof general topology ([1]). Rosenfeld ([6]) constituted a similar application tothe elementary theory of groupoids and groups. Xi ([7]) applied to the conceptof fuzzy set to BCK-algebras. Y. B. Jun and J. Meng ([4]) introduced of fuzzyp-ideals in BCI-algebras and studied their properties.In this paper, we introduce the notion of an enlarged p-ideal and a fuzzyp-ideal in BCI-algebras with degree. We study related properties of them.2. PreliminariesWe review some definitions and properties that will be useful in our results.By a BCI-algebra we mean an algebra (X,∗,0) of type (2,0) satisfying thefollowing conditions:(a1) (∀x,y,z ∈ X)(((x ∗y)∗(x ∗z))∗(z ∗y) = 0),(a2) (∀x,y ∈ X)((x ∗(x ∗y))∗y = 0),(a3) (∀x ∈ X)(x ∗x = 0),(a4) (∀x,y ∈ X)(x∗y = 0, y ∗x = 0 ⇒ x = y).If a BCI-algebra X satisfies the following identity:(a5) (∀x ∈ X)(0∗x = 0),then X is called a BCK-algebra.In any BCI-algebra X one can define a partial order “≤” by putting x ≤ yif and only if x ∗y = 0.A BCI-algebra X has the following properties:
TL;DR: In this paper, the integrability of various distributions of GCR-light-like submanifolds is established and conditions for the distributions to define totally geodesic foliations are obtained.
Abstract: In present paper we establish conditions for the integrability of various distributions of GCR-lightlike submanifolds and obtain conditions for the distributions to define totally geodesic foliations in GCR-lightlike submanifolds.
TL;DR: Comparison results of several types of the preconditioned Gauss-Seidel methods for solving a linear system whose coefficient matrix is a Z-matrix are provided.
Abstract: In this paper, we provide comparison results of several types of the preconditioned Gauss-Seidel methods for solving a linear system whose coefficient matrix is a Z-matrix. Lastly, numerical results are pre- sented to illustrate the theoretical results.
TL;DR: Using N-structures, the notion of an N-essence in a sub- traction algebra is introduced in this paper, and related properties of N-subalgebra are investigated.
Abstract: Using N-structures, the notion of an N-essence in a sub- traction algebra is introduced, and related properties are investigated. Relations among an N-ideal, an N-subalgebra and an N-essence are in- vestigated.
TL;DR: In this article, conditions for an N-subalgebra of type (∈,∈∨q) are considered and its characterizations are discussed, which are consistent with the asymmetry observation.
Abstract: . CharacterizationsofN-subalgebraoftype(∈,∈∨q)arepro-vided. ThenotionofN-subalgebrasoftype(∈,∈∨q)isintroduced,andits characterizations are discussed. Conditions for an N-subalgebra oftype(∈,∈∨q)(resp. (∈,∈∨q))tobeanN-subalgebraoftype(∈,∈)areconsidered. 1. IntroductionA (crisp) set A in a universe X can be defined in the form of its character-istic function µ A : X → {0,1} yielding the value 1 for elements belonging tothe set A and the value 0 for elements excluded from the set A. So far mostof the generalization of the crisp set have been conducted on the unit inter-val [0,1] and they are consistent with the asymmetry observation. In otherwords, the generalization of the crisp set to fuzzy sets relied on spreading pos-itive information that fit the crisp point {1} into the interval [0,1]. Because nonegative meaning of information is suggested, we now feel a need to deal withnegative information. To do so, we also feel a need to supply mathematicaltool. To attain such object, Jun et al. [5] introduced a new function whichis called negative-valued function, and constructed N-structures. They ap-plied N-structures to BCK/BCI-algebras, and discussed N-subalgebras andN-ideals in BCK/BCI-algebras. Jun et al. [6] considered closed ideals inBCH-algebras based on N-structures. Also, using N-structures, Jun and Leeintroduced the notion of an N-essence in a subtraction algebra, and inves-tigated related properties. They discussed relations among an N-ideal, anN-subalgebra and an N-essence (see [4]). To obtain more general form of anN-subalgebra in BCK/BCI-algebras, Jun et al. defined the notions of N-subalgebras of types (∈,∈), (∈, q), (∈,∈ ∨q), (q,∈), (q, q) and (q,∈ ∨q),and investigated related properties. They provided a characterization of an N-subalgebra of type (∈,∈∨q). They also gave conditions for an N-structure to
TL;DR: In this article, the superstability and generalized Hyers-Ulam stability of Jordan *-homomorphisms between unital -algebras associated with the following functional equation were proved.
Abstract: In this paper, we prove the superstability and the generalized Hyers-Ulam stability of Jordan *-homomorphisms between unital -algebras associated with the following functional equation. Morever, we investigate Jordan *-homomorphisms between unital -algebras associated with the following functional inequality .
TL;DR: In this article, the sum of a 2 F 1 obtained earlier by Lavoie et al. was derived with the help of generalization of Bailey's summation theorem on the sum.
Abstract: The aim of this research note is to provide the sums of theseriesX ∞k=0 (−1) k a−ik12 k (a+ + 1)for i = 0,±1,±2,±3,±4,±5 The results are obtained with the helpof generalization of Bailey’s summation theorem on the sum of a 2 F 1 obtained earlier by Lavoie et al Several interesting results includingthose obtained earlier by Srivastava, Vowe and Seiffert, follow specialcases of our main findings The results derived in this research note aresimple, interesting, easily established and (potentially) useful 1 Introduction and results requiredWe start with an interesting series due to Vowe and Seiffert [6]:(11) nX−1k=0 (−1) k n −1k12 k (n +k +1)=2 n (n −1)!n!(2n)!−1n2 n ;(n ∈ N= {1,2,3,})Vowe and Seiffert [6] obtained this interesting series by identifying the sumrelated to the following Eulerian integral(12)Z 10 1−t2 n− t n dtLater on, Srivastava [5] obtained the generalized (11) in the following form(13)X ∞k=0 (−1) k a−1k12 k (a +k +1)=2 a Γ(a)Γ(a+1)Γ(2a+1)−1a2
TL;DR: In this article, a non-linear semi-infinite programming problem is considered, where the functions involved are -semidifferentiable type I-preinvex and related functions.
Abstract: A nondifferentiable nonlinear semi-infinite programming problem is considered, where the functions involved are -semidifferentiable type I-preinvex and related functions. Necessary and sufficient optimality conditions are obtained for a nondifferentiable nonlinear semi-in nite programming problem. Also, a Mond-Weir type dual and a general Mond-Weir type dual are formulated for the nondifferentiable semi-infinite programming problem and usual duality results are proved using the concepts of generalized semilocally type I-preinvex and related functions.
TL;DR: For a bounded linear operator T, this paper showed that if T is algebraically (p,k)-quasihyponormal, then T is a- isoloid, polaroid, reguloid and a-polaroid.
Abstract: For a bounded linear operator T we prove the following as- sertions: (a) If T is algebraically (p;k)-quasihyponormal, then T is a- isoloid, polaroid, reguloid and a-polaroid. (b) If Tis algebraically (p;k)- quasihyponormal, then a-Weyl's theorem holds for f(T) for every f 2 Hol( (T)); where Hol( (T)) is the space of all functions that analytic in an open neighborhoods of (T) of T. (c) If Tis algebraically (p;k)- quasihyponormal, then generalized a-Weyl's theorem holds for f(T) for every f 2 Hol( (T)). (d) If T is a (p;k)-quasihyponormal operator, then the spectral mapping theorem holds for semi-B-essential approxi- mate point spectrum SBF+ (T); and for left Drazin spectrum lD(T) for every f 2 Hol( (T)):
TL;DR: In this article, the existence of (ϵ)-Lorentzian para-Sasakian mani- folds has been shown by an example. And in this paper, we study conformally at and Weyl-semisymmetric (σ, ϵ)-SASAKian manifolds.
Abstract: In this paper we study (ϵ)-Lorentzian para-Sasakian mani- folds and show its existence by an example. Some basic results regarding such manifolds have been deduced. Finally, we study conformally at and Weyl-semisymmetric (ϵ)-Lorentzian para-Sasakian manifolds.
TL;DR: In this article, the authors introduced the notions of Smarandache weak BE-algebra, Q-Smarandache √ √ ǫ √ Ω √ n, which is a Q-smarandaches upper set, and proved the relationship between these notions.
Abstract: . In this paper, we introduce the notions of Smarandache weakBE-algebra, Q-Smarandache filters and Q-Smarandache ideals. We showthat a nonempty subset F of a BE-algebra X is a Q-Smarandache filterif and only if A(x,y) ⊆F, which A(x,y) is a Q-Smarandache upper set.The relationship between these notions are stated and proved. 1. IntroductionThe Smarandache algebraic structures theory was introduced in 1998 byR. Padilla [9]. In [5], Kandasamy studied of Smarandache groupoids, sub-groupoids, ideal of groupoids, seminormal sub-groupoids, Smarandache Bolgroupoids, and strong Bol groupoids and obtained many interesting resultsabout them. Smarandache semigroups are very important for the study ofcongruences, and they were studied by Padilla [9].A Smarandache weak structure on a set S means a structure on S that hasa proper subset P with a weaker structure. By proper subset of a set S, wemean a subset P of S, different from the empty set, from the original set S,and from the idempotent elements if any.In [4], Borumand Saeid et al. studied the concept of Smarandache BCH-algebrasand obtainedmanyinterestingresultsabout Smarandache(fresh, cleanand fantastic) ideal in a BCH-algebras. Smarandache BL-algebras have beeninvented by Borumand Saeid et al. [3], and they dealed with Smarandache idealstructures in Smarandache BL-algebras.Recently, H. S. Kim and Y. H. Kim defined a BE-algebra [6]. S. S. Ahnand K. S. So defined the notion of ideals in BE-algebras, and then stated andproved several characterizationsof such ideals [2]. In [8], B. L. Meng introducedthe notion of an CI-algebra as a generalization of a BE-algebra.