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 Combined Relations between Contractive Mappings, Kannan Mappings, Reasonable | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 815637 25 pages doi 2009 815637 Research Article Some Combined Relations between Contractive Mappings Kannan Mappings Reasonable Expansive Mappings and T-Stability M. De la Sen Institute of Research and Development of Processes Faculty of Science and Technology University of the Basque Country Campus de Leioa Bizkaia Apertado 644 de Bilbao 48080 Bilbao Spain Correspondence should be addressed to M. De la Sen Received 13 May 2009 Accepted 31 August 2009 Recommended by Andrzej Szulkin In recent literature concerning fixed point theory for self-mappings T X X in metric spaces X d there are some new concepts which can be mutually related so that the inherent properties of each one might be combined for such self-mappings. Self-mappings T X X can be referred to for instance as Kannan-mappings reasonable expansive mappings and Picard T-stable mappings. Some relations between such concepts subject either to sufficient necessary or necessary and sufficient conditions are obtained so that in certain self-mappings can exhibit combined properties being inherent to each of its various characterizations. Copyright 2009 M. De la Sen. 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 As it is wellknown fixed point theory and related techniques are of increasing interest for solving a wide class of mathematical problems where convergence of a trajectory or sequence to some equilibrium set is essential see . 1-7 . Some of the specific topics recently covered in the field of fixed point theory are for instance as follows. 1 The properties of the so-called n-times reasonably expansive mapping are investigated in 1 in complete metric spaces X d as those fulfilling the property that d x Tnx
