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 Fixed Point Theorems for Suzuki Generalized Nonexpansive Multivalued Mappings in Banach Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 457935 10 pages doi 2010 457935 Research Article Fixed Point Theorems for Suzuki Generalized Nonexpansive Multivalued Mappings in Banach Spaces A. Abkar and M. Eslamian Department of Mathematics Imam Khomeini International University 288 Qazvin 34149 Iran Correspondence should be addressed to M. Eslamian mhmdeslamian@ Received 1 March 2010 Accepted 17 June 2010 Academic Editor Tomas Dominguez Benavides Copyright 2010 A. Abkar and M. Eslamian. 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. In the first part of this paper we prove the existence of common fixed points for a commuting pair consisting of a single-valued and a multivalued mapping both satisfying the Suzuki condition in a uniformly convex Banach space. In this way we generalize the result of Dhompongsa et al. 2006 . In the second part of this paper we prove a fixed point theorem for upper semicontinuous mappings satisfying the Suzuki condition in strictly L r spaces our result generalizes a recent result of Dominguez-Benavides et al. 2009 . 1. Introduction A mapping T on a subset E of a Banach space X is said to be nonexpansive if Tx - Ty x - y x y e E. In 2008 Suzuki 1 introduced a condition which is weaker than nonexpansiveness. Suzuki s condition which was named by him the condition C reads as follows a mapping T is said to satisfy the condition C on E if 1 2 x - Tx x - y IITx - Ty x - y x y e E. L2 He then proved some fixed point and convergence theorems for such mappings. We shall at times refer to this concept by saying that T is a generalized nonexpansive mapping in 2 Fixed Point Theory and Applications the sense of Suzuki. Very recently the current authors used a modified Suzuki condition for multivalued mappings and .
