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: Research Article Krasnosel’skii-Type Fixed-Set Results M. A. Al-Thagafi and Naseer Shahzad | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 394139 9 pages doi 2010 394139 Research Article Krasnosel skii-Type Fixed-Set Results M. A. Al-Thagafi and Naseer Shahzad Department of Mathematics King Abdulaziz University . Box 80203 Jeddah 21589 Saudi Arabia Correspondence should be addressed to Naseer Shahzad nshahzad@ Received 8 February 2010 Revised 16 August 2010 Accepted 23 August 2010 Academic Editor W. A. Kirk Copyright 2010 M. A. Al-Thagafi and N. 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. 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. 1. Introduction The Krasnosel skii fixed-point theorem 1 is a well-known principle that generalizes the Schauder fixed-point theorem and the Banach contraction principle as follows. Krasnosel skii Fixed-Point Theorem Let M be a nonempty closed convex subset of a Banach space E S M E and T M E. Suppose that a S is compact and continuous b T is a k-contraction c Sx Ty e M for every x y e M. Then there exists x e M such that Sx Tx x . This theorem has been extensively used in differential and functional differential equations and was motivated by the observation that the inversion of a perturbed differential operator may yield the sum of a continuous compact map and a contraction map. Note that the conclusion of the theorem does not need to hold if the convexity of M is relaxed even if T is the zero operator. Ok 2 noticed that the Krasnosel skii fixed-point theorem can be reformulated by relaxing or removing the convexity hypothesis of M and by allowing 2 Fixed Point
