tailieunhanh - Báo cáo hóa học: " Research Article Fixed Points of Weakly Contractive Maps and Boundedness of Orbits"

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 Points of Weakly Contractive Maps and Boundedness of Orbits | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2007 Article ID 20962 12 pages doi 2007 20962 Research Article Fixed Points of Weakly Contractive Maps and Boundedness of Orbits Jie-Hua Mai and Xin-He Liu Received 10 October 2006 Revised 8 January 2007 Accepted 31 January 2007 Recommended by William Art Kirk We discuss weakly contractive maps on complete metric spaces. Following three methods of generalizing the Banach contraction principle we obtain some fixed point theorems under some relatively weaker and more general contractive conditions. Copyright 2007 . Mai and . Liu. 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. 1. Introduction The Banach contraction principle is one of the most fundamental fixed point theorems. Theorem Banach contraction principle . Let X d be a complete metric space and let f X - X be a map. If there exists a constant c e 0 1 such that d f x f y c d x y then f has a unique fixed point u and lim .-V fn y u for each y e X. Since the publication of this result various authors have generalized and extended it by introducing weakly contractive conditions. In 1 Rhoades gathered 25 contractive conditions in order to compare them and obtain fixed point theorems. Collaco and Silva 2 presented a complete comparison for the maps numbered 1 - 25 by Rhoades 1 . One of the methods of alternating the Banach contractive condition is not to compare d f x f y with d x y but compare d fp x fq y with the distances between any two points in Op x f u Oq y f where p 1 and q 1 are given integers and Op x f x f x . fp x . see 3-6 . 2 Fixed Point Theory and Applications The generalized banach contraction conjecture was established in 7-10 of which the contractive condition is min d fk x fk y 1 k J c d x y where J is a positive integer. A further .