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Báo cáo hóa học: " Research Article Browder-Krasnoselskii-Type Fixed Point Theorems in Banach 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: Research Article Browder-Krasnoselskii-Type Fixed Point Theorems in Banach Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 243716 20 pages doi 10.1155 2010 243716 Research Article Browder-Krasnoselskii-Type Fixed Point Theorems in Banach Spaces Ravi P. Agarwal 1 2 Donal O Regan 3 and Mohamed-Aziz Taoudi4 1 Department of Mathematical Sciences Florida Institute of Technology 150 West University Boulevard Melbourne FL 32901 USA 2 Mathematics and Statistics Department King Fahd University of Petroleum and Minerals Dhahran 31261 Saudi Arabia 3 Department of Mathematics National University of Ireland Galway Ireland 4 Laboratoire de Mathematiques et de Dynamique de Populations Universite Cadi Ayyad Marrakech Morocco Correspondence should be addressed to Ravi P. Agarwal agarwal@fit.edu Received 29 January 2010 Accepted 6 July 2010 Academic Editor Hichem Ben-El-Mechaiekh Copyright 2010 Ravi P. Agarwal et al. 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. We present some fixed point theorems for the sum A B of a weakly-strongly continuous map and a nonexpansive map on a Banach space X. Our results cover several earlier works by Edmunds Reinermann Singh and others. 1. Introduction Let M be a nonempty subset of a Banach space X and T M X a mapping. We say that T is weakly-strongly continuous if for each sequence x in M which converges weakly to x in M the sequence Tx converges strongly to Tx. The mapping T is called nonexpansive if Tx - Ty x - y for all x y e M. In 1 Edmunds proved the following fixed point theorem Theorem 1.1. Let M be a nonempty bounded closed convex subset of a Hilbert space H and A B two maps from M into X such that i A is weakly-strongly continuous ii B is a nonexpansive mapping iii Ax By e M for all x y e M. Then A B has a fixed point in M. 2 Fixed Point Theory and Applications It is apparent that Theorem 1.1 is an important