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Báo cáo hóa học: " SEVERAL FIXED POINT THEOREMS CONCERNING τ-DISTANCE"

SEVERAL FIXED 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: POINT THEOREMS CONCERNING τ-DISTANCE | SEVERAL FIXED POINT THEOREMS CONCERNING T-DISTANCE TOMONARI SUZUKI Received 21 October 2003 and in revised form 10 March 2004 Using the notion of T-distance we prove several fixed point theorems which are generalizations of fixed point theorems by Kannan Meir-Keeler Edelstein and Nadler. We also discuss the properties of T-distance. 1. Introduction In 1922 Banach proved the following famous fixed point theorem 1 . Let X d be a complete metric space. Let T be a contractive mapping on X that is there exists r e 0 1 satisfying d Tx Ty rd x y 1.1 for all x y e X. Then there exists a unique fixed point x0 e X of T. This theorem called the Banach contraction principle is a forceful tool in nonlinear analysis. This principle has many applications and is extended by several authors Caristi 2 Edelstein 5 Ekeland 6 7 Meir and Keeler 14 Nadler 15 and others. These theorems are also extended see 4 9 10 13 23 25 26 27 and others. In 20 the author introduced the notion of T-distance and extended the Banach contraction principle Caristi s fixed point theorem and Ekeland s e-variational principle. In 1969 Kannan proved the following fixed point theorem 12 . Let X d be a complete metric space. Let T be a Kannan mapping on X that is there exists a e 0 1 2 such that d Tx Ty a d Tx x d Ty y 1.2 for all x y e X. Then there exists a unique fixed point x0 e X of T. We note that Kan-nan s fixed point theorem is not an extension of the Banach contraction principle. We also know that a metric space X is complete if and only if every Kannan mapping has a fixed point while there exists a metric space X such that X is not complete and every contractive mapping on X has a fixed point see 3 17 . Copyright 2004 Hindawi Publishing Corporation Fixed Point Theory and Applications 2004 3 2004 195-209 2000 Mathematics Subject Classification 54H25 54E50 URL http dx.doi.org 10.1155 S168718200431003X 196 Fixed point theorems concerning T-distance In this paper using the notion of T-distance we prove .