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Báo cáo hóa học: "COINCIDENCE POINT AND INVARIANT APPROXIMATION FOR MAPPINGS SATISFYING GENERALIZED WEAK CONTRACTIVE CONDITION"

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: COINCIDENCE POINT AND INVARIANT APPROXIMATION FOR MAPPINGS SATISFYING GENERALIZED WEAK CONTRACTIVE CONDITION | COINCIDENCE POINT AND INVARIANT APPROXIMATION FOR MAPPINGS SATISFYING GENERALIZED WEAK CONTRACTIVE CONDITION ISMAT BEG AND MUJAHID ABBAS Received 2 January 2006 Revised 14 February 2006 Accepted 22 February 2006 We prove the existence of coincidence point and common fixed point for mappings satisfying generalized weak contractive condition. As an application related results on invariant approximation are derived. Our results generalize various known results in the literature. Copyright 2006 I. Beg and M. Abbas. 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 and preliminaries Sessa 15 introduced the notion of weakly commuting maps in metric spaces. Jungck 8 coined the term of compatible mappings in order to generalize the concept of weak commutativity. Jungck and Rhoades 9 then defined a pair of self-mappings to be weakly compatible if they commute at their coincidence points. In recent years several authors used these concepts to obtain coincidence point results of various classes of mappings on a metric space. For a survey of coincidence point theory its applications and related results we refer to 1 4 5 10 13 . Meinardus 12 introduced the notion of invariant approximation. Brosowski 6 initiated the study of invariant approximation using fixed point theory and subsequently various interesting and valuable results applying fixed point theorems to obtain invariant approximation appeared in the literature of approximation theory see 3 7 16-18 . The aim of this paper is to present coincidence point result for two mappings which satisfy generalized weak contractive condition. Common fixed point theorem for a pair of weakly compatible maps which is more general than R-weakly commuting and compatible maps has also been proved. We also construct modified iterative procedures which converge to .