tailieunhanh - báo cáo hóa học:" Research Article A Common End Point Theorem for Set-Valued Generalized ψ, ϕ -Weak Contraction"

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 A Common End Point Theorem for Set-Valued Generalized ψ, ϕ -Weak Contraction | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 509658 8 pages doi 2010 509658 Research Article A Common End Point Theorem for Set-Valued Generalized y y -Weak Contraction Mujahid Abbas1 and Dragan Doric2 1 Department of Mathematics Centre for Advanced Studies in Mathematics Lahore University of Management Sciences 54792 Lahore Pakistan 2 Faculty of Organizational Sciences University of Belgrade Jove Ilica 154 11000 Beograd Serbia Correspondence should be addressed to Dragan Doric djoricd@ Received 21 August 2010 Accepted 18 October 2010 Academic Editor Satit Saejung Copyright 2010 M. Abbas and D. Doric. 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 introduce the class of generalized y y -weak contractive set-valued mappings on a metric space. We establish that such mappings have a unique common end point under certain weak conditions. The theorem obtained generalizes several recent results on single-valued as well as certain set-valued mappings. 1. Introduction and Preliminaries Alber and Guerre-Delabriere 1 defined weakly contractive maps on a Hilbert space and established a fixed point theorem for such a map. Afterwards Rhoades 2 using the notion of weakly contractive maps obtained a fixed point theorem in a complete metric space. Dutta and Choudhury 3 generalized the weak contractive condition and proved a fixed point theorem for a selfmap which in turn generalizes theorem 1 in 2 and the corresponding result in 1 . The study of common fixed points of mappings satisfying certain contractive conditions has been at the center of vigorous research activity. Beg and Abbas 4 obtained a common fixed point theorem extending weak contractive condition for two maps. In this direction Zhang and Song 5 introduced the concept of a generalized -weak .