tailieunhanh - Báo cáo hóa học: " An implicit iterative algorithm with errors for two families of generalized asymptotically nonexpansive mappings"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : An implicit iterative algorithm with errors for two families of generalized asymptotically nonexpansive mappings | Agarwal et al. Fixed Point Theory and Applications 2011 2011 58 http content 2011 1 58 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access An implicit iterative algorithm with errors for two families of generalized asymptotically nonexpansive mappings Ravi P Agarwal 1 Xiaolong Qin2 and Shin Min Kang3 Correspondence smkang@gnu. department of Mathematics and RINS Gyeongsang National University Jinju 660-701 Korea Full list of author information is available at the end of the article Springer Abstract In this paper an implicit iterative algorithm with errors is considered for two families of generalized asymptotically nonexpansive mappings. Strong and weak convergence theorems of common fixed points are established based on the implicit iterative algorithm. Mathematics Subject Classification 2000 47H09 47H10 47J25 Keywords Asymptotically nonexpansive mapping common fixed point implicit iterative algorithm generalized asymptotically nonexpansive mapping 1 Introduction In nonlinear analysis theory due to applications to complex real-world problems a growing number of mathematical models are built up by introducing constraints which can be expressed as subproblems of a more general problem. These constraints can be given by fixed-point problems see for example 1-3 . Study of fixed points of nonlinear mappings and its approximation algorithms constitutes a topic of intensive research efforts. Many well-known problems arising in various branches of science can be studied by using algorithms which are iterative in their nature. The well-known convex feasibility problem which captures applications in various disciplines such as image restoration computer tomography and radiation therapy treatment planning is to find a point in the intersection of common fixed point sets of a family of nonexpan-sive mappings see for example 3-5 . For iterative algorithms the most oldest and simple one is Picard .