Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 394139, 9 pages
doi:10.1155/2010/394139
Research Article

Krasnosel'skii-Type Fixed-Set Results

M. A. Al-Thagafi and Naseer Shahzad

Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 8 February 2010; Revised 16 August 2010; Accepted 23 August 2010

Academic Editor: W. A. Kirk

Copyright © 2010 M. A. Al-Thagafi and Naseer Shahzad. 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

Some new Krasnosel'skii-type fixed-set theorems are proved for the sum 𝑆 + 𝑇 , where 𝑆 is a multimap and 𝑇 is a self-map. The common domain of 𝑆 and 𝑇 is not convex. A positive answer to Ok's question (2009) is provided. Applications to the theory of self-similarity are also given.