tailieunhanh - Báo cáo hóa học: " Erratum Common Fixed Point Theorems for Hybrid Pairs of Occasionally Weakly Compatible Mappings Satisfying "

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: Erratum Common Fixed Point Theorems for Hybrid Pairs of Occasionally Weakly Compatible Mappings Satisfying | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 274793 2 pages doi 2008 274793 Erratum Common Fixed Point Theorems for Hybrid Pairs of Occasionally Weakly Compatible Mappings Satisfying Generalized Contractive Condition of Integral Type Revisited M. Abbas1 and B. E. Rhoades2 1 Centre for Advanced Studies in Mathematics and Department of Mathematics Lahore University of Management Sciences Lahore 54792 Pakistan 2 Department of Mathematics Indiana University Bloomington IN 47405 USA Correspondence should be addressed to B. E. Rhoades rhoades@ Received 3 September 2008 Accepted 30 September 2008 Copyright 2008 M. Abbas and B. E. Rhoades. 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 are indebted to Valeriu Popa for pointing out our error in 1 . In looking again at the paper we came up with the following example. Let X 0 1 with the usual metric and define f g X X T X CB X by fx 1 - x Tx 0 1 . Since f g every point is a coincidence point and fTx Tfx. Also H Tx Ty 0 for all x and y and dffx gy 0 for x y so f and T satisfy the hypotheses of all theorems and corollaries in 1 but f and T have no common fixed point. Thus it is not surprising that there are a number of papers involving hybrid pairs in which the conclusion of the theorems is not a common fixed point but a common coincidence point see . 2-10 . To obtain a common fixed point a number of theorems assume the strong condition that the common coincidence point is also a fixed point of one of the maps. References 1 M. Abbas and B. E. Rhoades Common fixed point theorems for hybrid pairs of occasionally weakly compatible mappings satisfying generalized contractive condition of integral type Fixed Point Theory and Applications vol. 2007 Article ID 54101 9 pages 2007. 2 A. Constantin .