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: Common fixed point and invariant approximation in hyperbolic ordered metric spaces | Abbas et al. Fixed Point Theory and Applications 2011 2011 25 http content 2011 1 25 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Common fixed point and invariant approximation in hyperbolic ordered metric spaces Mujahid Abbas1 Mohamed Amine Khamsi2 3 and Abdul Rahim Khan3 Correspondence arahim@kfupm. department of Mathematics and Statistics King Fahd University of Petroleum and Minerals Dhahran 31261 Saudi Arabia Full list of author information is available at the end of the article Springer Abstract We prove a common fixed point theorem for four mappings defined on an ordered metric space and apply it to find new common fixed point results. The existence of common fixed points is established for two or three noncommuting mappings where T is either ordered S-contraction or ordered asymptotically S-nonexpansive on a nonempty ordered starshaped subset of a hyperbolic ordered metric space. As applications related invariant approximation results are derived. Our results unify generalize and complement various known comparable results from the current literature. 2010 Mathematics Subject Classification 47H09 47H10 47H19 54H25. Keywords Hyperbolic metric space common fixed point Ordered uniformly Cq-commuting mapping ordered asymptotically S-nonexpansive mapping Best approximation 1 Introduction Metric fixed point theory has primary applications in functional analysis. The interplay between geometry of Banach spaces and fixed point theory has been very strong and fruitful. In particular geometric conditions on underlying spaces play a crucial role for finding solution of metric fixed point problems. Although it has purely metric flavor it is still a major branch of nonlinear functional analysis with close ties to Banach space geometry see for example 1-4 and references mentioned therein. Several results regarding existence and approximation of a fixed point of a mapping rely on convexity .
