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báo cáo hóa học:" Research Article Property P in 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 Property P in G-Metric Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 401684 12 pages doi 10.1155 2010 401684 Research Article Property P in G-Metric Spaces Renu Chugh 1 Tamanna Kadian 1 Anju Rani 1 and B. E. Rhoades2 1 Department of Mathematics Maharshi Dayanand University Rohtak 124001 India 2 Department of Mathematics Indiana University Bloomington IN 47405-7106 USA Correspondence should be addressed to Renu Chugh chughrenu@yahoo.com Received 19 December 2009 Revised 1 May 2010 Accepted 13 May 2010 Academic Editor Brailey Sims Copyright 2010 Renu Chugh 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. We prove two general fixed theorems for maps in G-metric spaces and then show that these maps satisfy property P . 1. Introduction Metric fixed point theory is an important mathematical discipline because of its applications in areas such as variational and linear inequalities optimization and approximation theory. Generalizations of metric spaces were proposed by Gahler 1 2 called 2-metric spaces and Dhage 3 4 called D-metric spaces . Hsiao 5 showed that for every contractive definition with xn Tnx0 every orbit is linearly dependent thus rendering fixed point theorems in such spaces trivial. Unfortunately it was shown that certain theorems involving Dhage s D-metric spaces are flawed and most of the results claimed by Dhage and others are invalid. These errors were pointed out by Mustafa and Sims in 6 among others. They also introduced a valid generalized metric space structure which they call G-metric spaces. Some other papers dealing with G-metric spaces are those in 7-11 . Let T be a self-map of a complete metric space X d with a nonempty fixed point set F T . Then T is said to satisfy property P if F T F Tn for each n e N. An interesting fact about maps satisfying property P