DSpace collection: 第47卷第4期

EXISTENCE THEOREMS FOR GENERALIZED VECTOR EQUILIBRIA WITH VARIABLE ORDERING RELATION

Tue, 17 Jan 2017 01:27:37 GMT

title: EXISTENCE THEOREMS FOR GENERALIZED VECTOR EQUILIBRIA WITH VARIABLE ORDERING RELATION abstract: In this paper we study the solvability of the generalized vector equilibrium problem (for short, GVEP) with a variable ordering relation in reflexive Banach spaces. The existence results of strong solutions of GVEPs for monotone multifunctions are established with the use of the KKM-Fan theorem. We also investigate the GVEPs without monotonicity assumptions and obtain the corresponding results of weak solutions by applying the Brouwer fixed point theorem. These results are also the extension and improvement of some recent results in the literature.

A NEW GENERAL IDEA FOR STARLIKE AND CONVEX FUNCTIONS

Tue, 17 Jan 2017 01:23:42 GMT

title: A NEW GENERAL IDEA FOR STARLIKE AND CONVEX FUNCTIONS abstract: Let AA be the class of functions f(z)f(z) which are analytic in the open unit disk UU with f(0)=0f(0)=0 and f′(0)=1f′(0)=1. For the class AA, a new general class AkAk is defined. With this general class AkAk, two interesting classes S∗k(α)Sk∗(α) and Kk(α)Kk(α) concerning classes of starlike of order αα in UU and convex of order αα in UU are considered.

ISOTROPIC GEOMETRY OF GRAPH SURFACES ASSOCIATED WITH PRODUCT PRODUCTION FUNCTIONS IN ECONOMICS

Tue, 17 Jan 2017 01:21:43 GMT

title: ISOTROPIC GEOMETRY OF GRAPH SURFACES ASSOCIATED WITH PRODUCT PRODUCTION FUNCTIONS IN ECONOMICS abstract: A production function is a mathematical formalization in economics which denotes the relations between the output generated by a firm, an industry or an economy and the inputs that have been used in obtaining it. In this paper, we study the product production functions of 2 variables in terms of the geometry of their associated graph surfaces in the isotropic 3−3−space I3I3. In particular, we derive several classification results for the graph surfaces of product production functions in I3I3 with constant curvature.

THE ROMAN BONDAGE NUMBER OF A DIGRAPH

Tue, 17 Jan 2017 01:19:46 GMT

title: THE ROMAN BONDAGE NUMBER OF A DIGRAPH abstract: Let D=(V,A)D=(V,A) be a finite and simple digraph. A Roman dominating function on DD is a labeling f:V(D)→{0,1,2}f:V(D)→{0,1,2} such that every vertex with label 0 has an in-neighbor with label 2. The weight of an RDF ff is the value ω(f)=∑v∈Vf(v)ω(f)=∑v∈Vf(v). The minimum weight of a Roman dominating function on a digraph DD is called the Roman domination number, denoted by γR(D)γR(D). The Roman bondage number bR(D)bR(D) of a digraph DD with maximum out-degree at least two is the minimum cardinality of all sets A′⊆AA′⊆A for which γR(D−A′)>γR(D)γR(D−A′)>γR(D). In this paper, we initiate the study of the Roman bondage number of a digraph. We determine the Roman bondage number in several classes of digraphs and give some sharp bounds.

EULER-CES`ARO DIFFERENCE SPACES OF BOUNDED, CONVERGENT AND NULL SEQUENCES

Tue, 17 Jan 2017 01:17:13 GMT

title: EULER-CES`ARO DIFFERENCE SPACES OF BOUNDED, CONVERGENT AND NULL SEQUENCES abstract: In this paper, we introduce the spaces ℓ˘∞ℓ˘∞, c˘c˘ and c˘0c˘0 of Euler-Ces`aro bounded, convergent and null difference sequences and prove that the inclusions ℓ∞⊂ℓ˘∞ℓ∞⊂ℓ˘∞, c⊂c˘c⊂c˘ and c0⊂c˘0c0⊂c˘0 strictly hold. We show that the spaces c˘0c˘0 and c˘c˘ turn out to be the separable BK spaces such that c˘c˘ does not possess any of the following: AK property and monotonicity. We determine the alpha-, beta- and gamma-duals of the new spaces and characterize the matrix classes (c˘:ℓ∞)(c˘:ℓ∞), (c˘:c)(c˘:c) and (c˘:c0)(c˘:c0).

EXTREME MONOPHONIC GRAPHS AND EXTREME GEODESIC GRAPHS

Tue, 17 Jan 2017 01:14:33 GMT

title: EXTREME MONOPHONIC GRAPHS AND EXTREME GEODESIC GRAPHS abstract: For a connected graph G=(V,E)G=(V,E) of order at least two, a chord of a path PP is an edge joining two non-adjacent vertices of PP. A path PP is called a monophonic path if it is a chordless path. A monophonic set of GG is a set SS of vertices such that every vertex of GG lies on a monophonic path joining some pair of vertices in SS. The monophonic number of GG is the minimum cardinality of its monophonic sets and is denoted by m(G)m(G). A geodetic set of GG is a set SS of vertices such that every vertex of GG lies on a geodesic joining some pair of vertices in SS. The geodetic number of GG is the minimum cardinality of its geodetic sets and is denoted by g(G)g(G). The number of extreme vertices in GG is its extreme order ex(G)ex(G). A graph GG is an extreme monophonic graph if m(G)=ex(G)m(G)=ex(G) and an extreme geodesic graph if g(G)=ex(G)g(G)=ex(G). Extreme monophonic graphs of order pp with monophonic number pp and p−1p−1 are characterized. It is shown that every pair a,ba,b of integers with 0≤a≤b0≤a≤b is realized as the extreme order and monophonic number, respectively, of some graph. For positive integers r,dr,d and k≥3k≥3 with r

EXTENDED CONSTANT PARTS OF BECKER-STARK'S AND SHAFER-FINK'S INEQUALITIES

Tue, 17 Jan 2017 01:12:19 GMT

title: EXTENDED CONSTANT PARTS OF BECKER-STARK'S AND SHAFER-FINK'S INEQUALITIES abstract: In this paper, we give some inequalities which are extended constant parts of Becker-Stark's and Shafer-Fink's inequality.

ON SEMI-SYMMETRIC METRIC CONNECTION IN SUB-RIEMANNIAN MANIFOLD

Tue, 17 Jan 2017 01:06:55 GMT

title: ON SEMI-SYMMETRIC METRIC CONNECTION IN SUB-RIEMANNIAN MANIFOLD abstract: The authors firstly in this paper define a semi-symmetric metric non-holonomic connection (in briefly, SS-connection) on sub-Riemannian manifolds. An invariant under a SS-connection transformation is obtained. The authors then further give a result that a sub-Riemannian manifold (M,V0,g,∇¯)(M,V0,g,∇¯) is locally horizontally flat if and only if MM is horizontally conformally flat and horizontally Ricci flat.