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 Strong Convergence of an Implicit Algorithm in CAT(0) Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 173621 11 pages doi 2011 173621 Research Article Strong Convergence of an Implicit Algorithm in CAT 0 Spaces Hafiz Fukhar-ud-din 1 Abdul Aziz Domlo 2 and Abdul Rahim Khan3 1 Department of Mathematics The Islamia University of Bahawalpur Bahawalpur 63100 Pakistan 2 Department of Mathematics Taibah University Madinah Munawarah 30002 Saudi Arabia 3 Department of Mathematics and Statistics King Fahd University of Petroleum and Minerals Dhahran 31261 Saudi Arabia Correspondence should be addressed to Abdul Rahim Khan arahim@ Received 23 November 2010 Accepted 23 December 2010 Academic Editor Qamrul Hasan Ansari Copyright 2011 Hafiz Fukhar-ud-din et al. 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. We establish strong convergence of an implicit algorithm to a common fixed point of a finite family of generalized asymptotically quasi-nonexpansive maps in CAT 0 spaces. Our work improves and extends several recent results from the current literature. 1. Introduction A metric space X d is said to be a length space if any two points of X are joined by a rectifiable path . a path of finite length and the distance between any two points of X is taken to be the infimum of the lengths of all rectifiable paths joining them. In this case d is said to be a length metric otherwise known as an inner metric or intrinsic metric . In case no rectifiable path joins two points of the space the distance between them is taken to be TO. A geodesic path joining x e X to y e X or more briefly a geodesic from x to y is a map c from a closed interval 0 c R to X such that c 0 x c l y and d c t c f f - f for all t f e 0 l . In particular c is an isometry and d x y l. The image a of c is called a geodesic or metric segment .
