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 On Mappings with Contractive Iterate at a Point in Generalized Metric Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 458086 16 pages doi 2010 458086 Research Article On Mappings with Contractive Iterate at a Point in Generalized Metric Spaces Ljiljana Gajic and Zagorka Lozanov-Crvenkovic Department of Mathematics and Informatics University of Novi Sad Trg Dositeja Obradovba 4 21000 Novi Sad Serbia Correspondence should be addressed to Ljiljana Gajic gajic@ Received 7 September 2010 Revised 1 December 2010 Accepted 29 December 2010 Academic Editor B. Rhoades Copyright 2010 L. Gajic and Z. Lozanov-Crvenkovic. 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. Using the setting of generalized metric space the so-called G-metric space fixed point theorems for mappings with a contractive and a generalized contractive iterate at a point are proved. These results generalize some comparable results in the literature. A common fixed point result is also proved. 1. Introduction Sehgal in 1 proved fixed point theorem for mappings with a contractive iterate at a point and therefore generalized a well-known Banach theorem. Theorem . Let X d be a complete metric space and let T X X be a continuous mapping with property that for every x e X there exists n x e N so that for every y e X dfiTntx x G d x where e 0-11. x y G q x y OVeie q . . Then T has a unique fixed point u in X and limfcTfc x0 u for each x0 e X. Guseman 2 extended Sehgal s result by removing the condition of continuity of T and weakening to hold on some subset B of X such that T B c B where for some x0 e B B contains the closure of the iterates of x0. Further extensions appear in 3 4 . Our aim in this study is to show that these results are valid in more general class of spaces. In 1963 S. Gahler introduced the notion of 2-metric spaces but .
