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Báo cáo hóa học: " Research Article Fixed Point Theorems for ws-Compact Mappings 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 Fixed Point Theorems for ws-Compact Mappings in Banach Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 183596 13 pages doi 10.1155 2010 183596 Research Article Fixed Point Theorems for ws-Compact Mappings 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 Universite Cadi Ayyad Laboratoire de Mathématiques et de Dynamique de Populations Marrakech Morocco Correspondence should be addressed to Ravi P. Agarwal agarwal@fit.edu Received 17 August 2010 Revised 21 October 2010 Accepted 4 November 2010 Academic Editor Jerzy Jezierski 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 new fixed point theorems for ws-compact operators. Our fixed point results are obtained under Sadovskii Leray-Schauder Rothe Altman Petryshyn and Furi-Pera type conditions. An example is given to show the usefulness and the applicability of our results. 1. Introduction Let X be a Banach space and let M be a subset of X. Following 1 a map A M X is said to be ws-compact if it is continuous and for any weakly convergent sequence x eN in M the sequence Ax eN has a strongly convergent subsequence in X. This concept arises naturally in the study of both integral and partial differential equations see 1-5 . In this paper we continue the study of ws-compact mappings investigate the boundary conditions and establish new fixed point theorems. Specifically we prove several fixed point theorems for ws-compact mappings under Sadovskii Leray-Schauder Rothe Altman Petryshyn and .