tailieunhanh - Báo cáo hóa học: " A generalised fixed point theorem of Presic type in cone metric spaces and application to Markov process"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : A generalised fixed point theorem of Presic type in cone metric spaces and application to Markov process | George et al. Fixed Point Theory and Applications 2011 2011 85 http content 2011 1 85 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access A generalised fixed point theorem of Presic type in cone metric spaces and application to Markov process Reny George1 2 KP Reshma2 and R Rajagopalan 1 Correspondence renygeorge02@ department of Mathematics College of Science Al-Kharj University Al-Kharj Kingdom of Saudi Arabia Full list of author information is available at the end of the article Springer Abstract A generalised common fixed point theorem of Presic type for two mappings f X X and T Xk X in a cone metric space is proved. Our result generalises many well-known results. 2000 Mathematics Subject Classification 47H10 Keywords Coincidence and common fixed points cone metric space weakly compatible 1. Introduction Considering the convergence of certain sequences Presic 1 proved the following Theorem . Let X d be a metric space k a positive integer T Xk X be a mapping satisfying the following condition d T xi X2 . . Xk T X2 X3 . . . Xk 1 q d xi X2 q2 d X2 Xs - qk d xi Xk 1 where x1 x2 . xk 1 are arbitrary elements in X and q1 q2 . qk are non-negative constants such that q1 q2 qk 1. Then there exists some x e X such that x T x x . x . Moreover if x1 x2 . xk are arbitrary points in X and for n e N xn k T xn xn 1 . xn k-1 then the sequence xn is convergent and lim xn T lim xn lim xn . lim xn . Note that for k 1 the above theorem reduces to the well-known Banach Contraction Principle. Ciric and Presic 2 generalising the above theorem proved the following Theorem . Let X d be a metric space k a positive integer T Xk X be a mapping satisfying the following condition d T x1 X2 . Xk T x2 X3 . Xk 1 d x1 x2 d x2 x3 . d Xk Xk 1 where x1 x2 . xk 1 are arbitrary elements in X and l e 0 1 . Then there exists some x e X such that x T x x . x . Moreover if x1 x2 . xk are arbitrary points in X