tailieunhanh - Báo cáo hóa học: " Common fixed point theorems for generalized J H-operator classes and invariant approximations"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Common fixed point theorems for generalized J H-operator classes and invariant approximations | Sintunavarat and Kumam Journal of Inequalities and Applications 2011 2011 67 http content 2011 1 67 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Common fixed point theorems for generalized jw-operator classes and invariant approximations Wutiphol Sintunavarat and Room Kumam Correspondence poom. kum@ Department of Mathematics Faculty of Science King Mongkut s University of Technology Thonburi Kmutt Bangkok 10140 Thailand Springer Abstract In this article we introduce two new different classes of noncommuting selfmaps. The first class is more general than jw operator class of Hussain et al. Common fixed points for jw-operators and occasionally weakly biased pairs under relaxed conditions. Nonlinear Anal. 74 6 2133-2140 2011 and occasionally weakly compatible class. We establish the existence of common fixed point theorems for these classes. Several invariant approximation results are obtained as applications. Our results unify extend and complement several well-known results. 2000 Mathematical Subject Classification 47H09 47H10. Keywords common fixed point occasionally weakly compatible maps Banach operator pair R-operator pair JH-operator pair generalized JH-operator pair invariant approximation 1. Introduction The fixed point theorem generally known as the Banach contraction principle appeared in explicit form in Banach s thesis in 1922 1 where it was used to establish the existence of a solution for an integral equation. Since its simplicity and usefulness it has become a very popular tool in solving existence problems in many branches of mathematical analysis. Banach contraction principle has been extended in many different directions. Many authors established fixed point theorems involving more general contractive conditions. In 1976 Jungck 2 extend the Banach contraction principle to a common fixed point theorem for commuting maps. Sessa 3 defined the notion of .