. In this paper, we generalize the extended Appell’s and Lauricella’s hypergeometric functions which have recently been introduced by Liu [9] and Khan [7]. Also, we aim at establishing some (presumbly) new integral representations and transforms for the extended generalized Appell’s and Lauricella’s hypergeometric functions.
{"title":"Some integral representations and transforms for extended generalized Appell's and Lauricella's hypergeometric functions","authors":"Yongsup Kim","doi":"10.4134/CKMS.C160075","DOIUrl":"https://doi.org/10.4134/CKMS.C160075","url":null,"abstract":". In this paper, we generalize the extended Appell’s and Lauricella’s hypergeometric functions which have recently been introduced by Liu [9] and Khan [7]. Also, we aim at establishing some (presumbly) new integral representations and transforms for the extended generalized Appell’s and Lauricella’s hypergeometric functions.","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2017-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41802755","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"CORRIGENDUM TO \"A COMMON FIXED POINT THEOREM FOR T-CONTRACTIONS ON GENERALIZED CONE b-METRIC SPACES\", COMMUN. KOREAN MATH. SOC. 32 (2017), NO. 1, 65-74","authors":"M. Rangamma, P. M. Reddy","doi":"10.4134/CKMS.C170088","DOIUrl":"https://doi.org/10.4134/CKMS.C170088","url":null,"abstract":"","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2017-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46882431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract. In this paper, we utilize the Nevanlinna theory and uniqueness theory of meromorphic function to investigate the differential-difference analogue of Brück conjecture. In other words, we consider ∆ηf(z) = f(z+η)−f(z) and f (z) share one value or one small function, and then obtain the precise expression of transcendental entire function f(z) under certain conditions, where η ∈ C {0} is a constant such that f(z + η) − f(z) 6≡ 0.
{"title":"SOME RESULTS ON COMPLEX DIFFERENTIAL-DIFFERENCE ANALOGUE OF BRÜCK CONJECTURE","authors":"Min Chen, Zongsheng Gao","doi":"10.4134/CKMS.C160123","DOIUrl":"https://doi.org/10.4134/CKMS.C160123","url":null,"abstract":"Abstract. In this paper, we utilize the Nevanlinna theory and uniqueness theory of meromorphic function to investigate the differential-difference analogue of Brück conjecture. In other words, we consider ∆ηf(z) = f(z+η)−f(z) and f (z) share one value or one small function, and then obtain the precise expression of transcendental entire function f(z) under certain conditions, where η ∈ C {0} is a constant such that f(z + η) − f(z) 6≡ 0.","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2017-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46394351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. The purpose of this paper is to introduce some strong conver- gence theorems for the problem of finding a common zero of a finite family of monotone operators and the problem of finding a common fixed point of a finite family of nonexpansive in Hilbert spaces by hybrid projection method.
{"title":"A HYBRID PROJECTION METHOD FOR COMMON ZERO OF MONOTONE OPERATORS IN HILBERT SPACES","authors":"Minh-Tuyen Truong","doi":"10.4134/CKMS.C160096","DOIUrl":"https://doi.org/10.4134/CKMS.C160096","url":null,"abstract":". The purpose of this paper is to introduce some strong conver- gence theorems for the problem of finding a common zero of a finite family of monotone operators and the problem of finding a common fixed point of a finite family of nonexpansive in Hilbert spaces by hybrid projection method.","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2017-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46456053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. We study the existence and uniqueness of S-asymptotically ω -periodic mild solutions for some partial functional integrodifferential equations with infinite delay and nonlocal conditions.
研究了一类具有有限时滞和非局部条件的偏泛函积分微分方程S-渐近ω-周期温和解的存在性和唯一性。
{"title":"THE EXISTENCE OF S-ASYMPTOTICALLY ω-PERIODIC MILD SOLUTIONS FOR SOME DIFFERENTIAL EQUATION WITH NONLOCAL CONDITIONS","authors":"Hyun Ho Jang, H. Lee","doi":"10.4134/CKMS.C160104","DOIUrl":"https://doi.org/10.4134/CKMS.C160104","url":null,"abstract":". We study the existence and uniqueness of S-asymptotically ω -periodic mild solutions for some partial functional integrodifferential equations with infinite delay and nonlocal conditions.","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2017-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44868486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"INCOMPLETE EXTENDED HURWITZ-LERCH ZETA FUNCTIONS AND ASSOCIATED PROPERTIES","authors":"R. K. Parmar, R. Saxena","doi":"10.4134/CKMS.C150227","DOIUrl":"https://doi.org/10.4134/CKMS.C150227","url":null,"abstract":"","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2017-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42315314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. H. R. Ebrahimi Vishki et al. conjectured in [1], that if every Jordan higher derivation on a trivial generalized matrix algebra G = ( A,M,N,B ) is a higher derivation, then either M = 0 or N = 0. In this note, we will give a class of counter examples.
{"title":"A NOTE ON JORDAN DERIVATIONS OF TRIVIAL GENERALIZED MATRIX ALGEBRAS","authors":"Yanbo Li, Chenyou Zheng","doi":"10.4134/CKMS.C160091","DOIUrl":"https://doi.org/10.4134/CKMS.C160091","url":null,"abstract":". H. R. Ebrahimi Vishki et al. conjectured in [1], that if every Jordan higher derivation on a trivial generalized matrix algebra G = ( A,M,N,B ) is a higher derivation, then either M = 0 or N = 0. In this note, we will give a class of counter examples.","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2017-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44513233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The aim of this paper is to investigate locally φ-conformally symmetric almost Kenmotsu manifolds with its characteristic vector field ξ belonging to some nullity distributions. Also, we give an example of a 5-dimensional almost Kenmotsu manifold such that ξ belongs to the (k, μ)′-nullity distribution and h′ 6= 0.
{"title":"ON LOCALLY 𝜙-CONFORMALLY SYMMETRIC ALMOST KENMOTSU MANIFOLDS WITH NULLITY DISTRIBUTIONS","authors":"U. De, K. Mandal","doi":"10.4134/CKMS.C160073","DOIUrl":"https://doi.org/10.4134/CKMS.C160073","url":null,"abstract":"The aim of this paper is to investigate locally φ-conformally symmetric almost Kenmotsu manifolds with its characteristic vector field ξ belonging to some nullity distributions. Also, we give an example of a 5-dimensional almost Kenmotsu manifold such that ξ belongs to the (k, μ)′-nullity distribution and h′ 6= 0.","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2017-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47616487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let D be a directed graph with p vertices and q arcs. A vertex out-magic total labeling is a bijection f from V (D) ∪ A(D) −→ {1, 2, . . ., p + q} with the property that for every v ∈ V (D), f(v) + ∑ u∈O(v) f((v, u)) = k, for some constant k. Such a labeling is called a V super vertex outmagic total labeling (V -SVOMT labeling) if f(V (D)) = {1, 2, 3, . . . , p}. A digraph D is called a V -super vertex out-magic total digraph (V -SVOMT digraph) if D admits a V -SVOMT labeling. In this paper, we provide a method to find the most vital nodes in a network by introducing the above labeling and we study the basic properties of such labelings for digraphs. In particular, we completely solve the problem of finding V -SVOMT labeling of generalized de Bruijn digraphs which are used in the interconnection network topologies. 1. Background A labeling of a graph G is a mapping that carries a set of graph elements, usually the vertices and edges into a set of numbers, usually integers. We deal with digraphs which possibly admit self-loops but not multiple arcs. For standard graph theory terminology we follow [6]. Specifically, let D = (V,A) be a digraph with vertex set V and arc set A. If (u, v) ∈ A, then there is an arc from u to v and u is called a head, v is called a tail. If (u, u) ∈ A, the arc (u, u) is called a self-loop or loop. For a vertex v ∈ V, the sets O(v) = {u | (v, u) ∈ A} and I(v) = {u | (u, v) ∈ A} are called the out-neighborhood and the inneighborhood of the vertex v, respectively. The out-degree and in-degree of v are deg(v) = |O(v)| and deg(v) = |I(v)|, respectively. MacDougall et al. [12, 15] introduced the notion of vertex magic total labeling. If G is a finite simple undirected graph with p vertices and q edges, then a vertex magic total labeling is a bijection f from V (G) ∪ E(G) to the integers 1, 2, . . . , p + q with the property that for every u in V (G), f(u) + Received October 20, 2015. 2010 Mathematics Subject Classification. Primary 05C78.
{"title":"V-SUPER VERTEX OUT-MAGIC TOTAL LABELINGS OF DIGRAPHS","authors":"G. D. Devi, M. Durga, G. Marimuthu","doi":"10.4134/CKMS.C150189","DOIUrl":"https://doi.org/10.4134/CKMS.C150189","url":null,"abstract":"Let D be a directed graph with p vertices and q arcs. A vertex out-magic total labeling is a bijection f from V (D) ∪ A(D) −→ {1, 2, . . ., p + q} with the property that for every v ∈ V (D), f(v) + ∑ u∈O(v) f((v, u)) = k, for some constant k. Such a labeling is called a V super vertex outmagic total labeling (V -SVOMT labeling) if f(V (D)) = {1, 2, 3, . . . , p}. A digraph D is called a V -super vertex out-magic total digraph (V -SVOMT digraph) if D admits a V -SVOMT labeling. In this paper, we provide a method to find the most vital nodes in a network by introducing the above labeling and we study the basic properties of such labelings for digraphs. In particular, we completely solve the problem of finding V -SVOMT labeling of generalized de Bruijn digraphs which are used in the interconnection network topologies. 1. Background A labeling of a graph G is a mapping that carries a set of graph elements, usually the vertices and edges into a set of numbers, usually integers. We deal with digraphs which possibly admit self-loops but not multiple arcs. For standard graph theory terminology we follow [6]. Specifically, let D = (V,A) be a digraph with vertex set V and arc set A. If (u, v) ∈ A, then there is an arc from u to v and u is called a head, v is called a tail. If (u, u) ∈ A, the arc (u, u) is called a self-loop or loop. For a vertex v ∈ V, the sets O(v) = {u | (v, u) ∈ A} and I(v) = {u | (u, v) ∈ A} are called the out-neighborhood and the inneighborhood of the vertex v, respectively. The out-degree and in-degree of v are deg(v) = |O(v)| and deg(v) = |I(v)|, respectively. MacDougall et al. [12, 15] introduced the notion of vertex magic total labeling. If G is a finite simple undirected graph with p vertices and q edges, then a vertex magic total labeling is a bijection f from V (G) ∪ E(G) to the integers 1, 2, . . . , p + q with the property that for every u in V (G), f(u) + Received October 20, 2015. 2010 Mathematics Subject Classification. Primary 05C78.","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2017-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47492184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this research work, by using the random resolvent operator techniques associated with random (At, ηt,mt)-monotone operators, is to established an existence and convergence theorems for a class of fuzzy system of random nonlinear equations with fuzzy mappings in Hilbert spaces. Our results improve and generalized the corresponding results of the recent works.
{"title":"ITERATIVE ALGORITHMS FOR A FUZZY SYSTEM OF RANDOM NONLINEAR EQUATIONS IN HILBERT SPACES","authors":"S. Salahuddin","doi":"10.4134/CKMS.C160088","DOIUrl":"https://doi.org/10.4134/CKMS.C160088","url":null,"abstract":"In this research work, by using the random resolvent operator techniques associated with random (At, ηt,mt)-monotone operators, is to established an existence and convergence theorems for a class of fuzzy system of random nonlinear equations with fuzzy mappings in Hilbert spaces. Our results improve and generalized the corresponding results of the recent works.","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2017-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42227858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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