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 A Common Fixed Point Theorem in D∗ -Metric Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2007 Article ID 27906 13 pages doi 2007 27906 Research Article A Common Fixed Point Theorem in D -Metric Spaces Shaban Sedghi Nabi Shobe and Haiyun Zhou Received 27 February 2007 Accepted 16 July 2007 Recommended by Thomas Bartsch We give some new definitions of D -metric spaces and we prove a common fixed point theorem for a class of mappings under the condition of weakly commuting mappings in complete D -metric spaces. We get some improved versions of several fixed point theorems in complete D -metric spaces. Copyright 2007 Shaban Sedghi 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 The concept of fuzzy sets was introduced initially by Zadeh 1 in 1965. Since then to use this concept in topology and analysis many authors have expansively developed the theory of fuzzy sets and applications. Especially Deng 2 Erceg 3 Kaleva and Seikkala 4 and Kramosil and Michalek 5 have introduced the concepts of fuzzy metric spaces in different ways. George and Veeramani 6 and Kramosil and Michalek 5 have introduced the concept of fuzzy topological spaces induced by fuzzy metric which have very important applications in quantum particle physics particularly in connection with both string and ff-infinity theories which were given and studied by El Naschie 7-10 . Many authors 11-17 have studied the fixed point theory in fuzzy probabilistic metric spaces. On the other hand there have been a number of generalizations of metric spaces. One of such generalizations is generalized metric space or D-metric space initiated by Dhage 18 in 1992. He proved the existence of unique fixed point of a self-map satisfying a contractive condition in complete and bounded D-metric spaces. Dealing with D-metricspace Ahmad et al. 19 Dhage
