tailieunhanh - Báo cáo hóa học: " Research Article Some Fixed Point Theorem for Mapping on Complete G-Metric Spaces"

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 Some Fixed Point Theorem for Mapping on Complete G-Metric Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 189870 12 pages doi 2008 189870 Research Article Some Fixed Point Theorem for Mapping on Complete G-Metric Spaces Zead Mustafa Hamed Obiedat and Fadi Awawdeh Department of Mathematics The Hashemite University . Box 330127 Zarqa 13115 Jordan Correspondence should be addressed to Zead Mustafa zmagablh@ Received 1 April 2008 Accepted 10 July 2008 Recommended by Brailey Sims We prove some fixed point results for mapping satisfying sufficient conditions on complete G-metric space also we showed that if the G-metric space X G is symmetric then the existence and uniqueness of these fixed point results follow from well-known theorems in usual metric space X dG where X dG is the usual metric space which defined from the G-metric space X G . Copyright 2008 Zead Mustafa 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. 1. Introduction During the sixties the notion of 2-metric space introduced by Gahler see 1 2 as a generalization of usual notion of metric space X d . But different authors proved that there is no relation between these two functions for instance Ha et al. in 3 show that 2-metric need not be continuous function further there is no easy relationship between results obtained in the two settings. In 1992 Bapure Dhage in his . thesis introduce a new class of generalized metric space called D-metric spaces 4 5 . In a subsequent series of papers Dhage attempted to develop topological structures in such spaces see 5-7 . He claimed that D-metrics provide a generalization of ordinary metric functions and went on to present several fixed point results. But in 2003 in collaboration with Brailey Sims we demonstrated in 8 that most of the claims concerning the fundamental topological structure of