Table of Contents
ISRN Applied Mathematics
Volume 2011 (2011), Article ID 696917, 13 pages
http://dx.doi.org/10.5402/2011/696917
Research Article

Some Results for the Family KKM(X,Y) and the Ξ¦-Mapping in FC-Spaces

Department of Mathematics, Chengdu University of Information Technology, Chengdu, Sichuan 610103, China

Received 15 July 2011; Accepted 24 August 2011

Academic Editor: A. Bellouquid

Copyright Β© 2011 Rong-Hua He. 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.

Abstract

We first establish a fixed point theorem for a π‘˜-set contraction map on the family 𝐾𝐾𝑀(𝑋,𝑋), which does not need to be a compact map. Next, we present the 𝐾𝐾𝑀 type theorems, matching theorems, coincidence theorems, and minimax theorems on the family 𝐾𝐾𝑀(𝑋,π‘Œ) and the Ξ¦-mapping in FC-spaces. Our results improve and generalize some recent results.