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Báo cáo hóa học: " Fixed point theory for cyclic (j - ψ)-contraction"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí sinh học đề tài : Fixed point theory for cyclic (j - ψ)-contraction | Karapinar and Sadarangani Fixed Point Theory and Applications 2011 2011 69 http www.fixedpointtheoryandapplications.eom content 2011 1 69 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Fixed point theory for cyclic j - -contractions Erdal Karapinar 1 and Kishin Sadarangani2 Correspondence erdalkarapinar@yahoo.com department of Mathematics Atilim University 06836 Incek Ankara Turkey Full list of author information is available at the end of the article Springer Abstract In this article the concept of cyclic j - -contraction and a fixed point theorem for this type of mappings in the context of complete metric spaces have been presented. The results of this study extend some fixed point theorems in literature. 2000 Mathematics Subject Classification 47H10 46T99 54H25. Keywords cyclic j - -contraction fixed point theory. 1. Introduction and preliminaries One of the most important results used in nonlinear analysis is the well-known Banach s contraction principle. Generalization of the above principle has been a heavily investigated branch research. Particularly in 1 the authors introduced the following definition. Definition 1. Let X be a nonempty set m a positive integer and T X X a mapping. X Ui jAi is said to be a cyclic representation of X with respect to T if i Ai i 1 2 . m are nonempty sets. ii T A1 c A 2 . T Am-1 c Am T Am c A1. Recently fixed point theorems for operators T defined on a complete metric space X with a cyclic representation of X with respect to T have appeared in the literature see e.g. 2-5 . Now we present the main result of 5 . Previously we need the following definition. Definition 2. Let X d be a metric space m a positive integer A1 A2 . Am nonempty closed subsets of X and X Ui jAi. An operator T X X is said to be a cyclic weak j-contraction if i X Ui jAiis a cyclic representation of X with respect to T. ii d Tx Ty d x y - j d x y for any X e Ai y e Ai 1 i 1 2 . m where Am 1 A1 and j 0 0 is a nondecreasing and