tailieunhanh - Báo cáo hóa học: "ON ALMOST COINCIDENCE POINTS IN GENERALIZED CONVEX SPACES"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: ON ALMOST COINCIDENCE POINTS IN GENERALIZED CONVEX SPACES | ON ALMOST COINCIDENCE POINTS IN GENERALIZED CONVEX SPACES ZORAN D. MITROVIC Received 19 April 2006 Accepted 7 June 2006 We prove an almost coincidence point theorem in generalized convex spaces. As an application we derive a result on the existence of a maximal element and an almost coincidence point theorem in hyperconvex spaces. The results of this paper generalize some known results in the literature. Copyright 2006 Zoran D. Mitrovic. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction and preliminaries The notion of a generalized convex space we work with in this paper was introduced by Park and Kim in 10 . In generalized convex spaces many results on fixed points coincidence points equilibrium problems variational inequalities continuous selections saddle points and others have been obtained see for example 6 8 10-13 . In this paper we obtain an almost coincidence point theorem in generalized convex spaces. Some applications to the existence of a maximal element of an almost fixed point theorem in hyperconvex spaces are given. A multimap or map F X Y is a function from a set X into the power set of a set Y. For A c X let F A u Fx x e A . For any B c Y the lower inverse and upper inverse of B under F are defined by F- B x e X Fx n B 0 F B x e X Fx c B respectively. The lower inverse of F X Y is the map F- Y X defined by x e F- y if and only if y e Fx. A map F X Y is upper lower semicontinuous on X if and only if for every open V c Y the set F V F- V is open. A map F X Y is continuous if and only if it is upper and lower semicontinuous. Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2006 Article ID 91397 Pages 1-7 DOI FPTA 2006 91397 2 On almost coincidence points For a nonempty subset D of X let D denote the set of all nonempty finite subsets of D. .

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