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: APPROXIMATING COMMON FIXED POINTS OF TWO ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACES | APPROXIMATING COMMON FIXED POINTS OF TWO ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACES NASEER SHAHZAD AND ANIEFIOK UDOMENE Received 21 April 2005 Revised 13 July 2005 Accepted 18 July 2005 Suppose K is a nonempty closed convex subset of a real Banach space E. Let s T K - K be two asymptotically quasi-nonexpansive maps with sequences un vn c 0 to such that Zn 1 un TO and Zn 1 vn TO and F F S n F T x G K Sx Tx x 0. Suppose xn is generated iteratively by x1 G K xn 1 1 - an xn ansn 1 - pn xn pnTnxn n 1 where an and fin are real sequences in 0 1 . It is proved that a xn converges strongly to some x G F if and only if liminfn TOd xn F 0 b if X is uniformly convex and if either T or S is compact then xn converges strongly to some x G F. Furthermore if X is uniformly convex either T or s is compact and xn is generated by x1 G K xn 1 nxn PnSn a nxn p nTnxn y nz n YnZn n 1 where Zn z n are bounded an fin yn a n fi n y n are real sequences in 0 1 such that an fin yn 1 a n pn y n and yn y are summable it is established that the sequence xn with error member terms converges strongly to some x G F. Copyright 2006 N. Shahzad and A. Udomene. 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 Let K be a nonempty subset of a real normed linear space E. Let T be a self-mapping of K. Then T is said to be asymptotically nonexpansive with sequence vn c 0 to if lim TO vn 0 and Tnx- Tny 1 v x-yll for all x y G K and n 1 and is said to be asymptotically quasi-nonexpansive with sequence vn c 0 to ifF T x G K Tx x 0 lim TO vn 0 and Tnx - x 1 v x- x Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2006 Article ID 18909 Pages 1-10 DOI FPTA 2006 18909 2 Approximating common fixed points forallx e K x e F T and n 1. The mapping T is called nonexpansive if Tx - Tyll x -
