tailieunhanh - Báo cáo hóa học: " Research Article Monotone Generalized Nonlinear Contractions in Partially Ordered 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 Monotone Generalized Nonlinear Contractions in Partially Ordered Metric Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 131294 11 pages doi 2008 131294 Research Article Monotone Generalized Nonlinear Contractions in Partially Ordered Metric Spaces Ljubomir Ciric 1 Nenad CakiC 2 Miloje RajoviC 3 and Jeong Sheok Ume4 1 Faculty of Mechanical Engineering University of Belgrade Kraljice Marije 16 11 000 Belgrade Serbia 2 Faculty of Electrical Engineering University of Belgrade Boulevard Kralja Aleksandra 73 11 000 Belgrade Serbia 3 Faculty of Mechanical Engineering University of Kragujevac Dositejeva 19 36 000 Kraljevo Serbia 4 Department of Applied Mathematics Changwon National University Changwon 641-773 South Korea Correspondence should be addressed to Ljubomir Ciric lciric@ Received 29 August 2008 Accepted 9 December 2008 Recommended by Juan Jose Nieto A concept of g-monotone mapping is introduced and some fixed and common fixed point theorems for g-non-decreasing generalized nonlinear contractions in partially ordered complete metric spaces are proved. Presented theorems are generalizations of very recent fixed point theorems due to Agarwal et al. 2008 . Copyright 2008 Ljubomir Ciric 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 Banach fixed point theorem for contraction mappings has been extended in many directions cf. 1-28 . Very recently Agarwal et al. 1 presented some new results for generalized nonlinear contractions in partially ordered metric spaces. The main idea in 1 20 26 involve combining the ideas of iterative technique in the contraction mapping principle with those in the monotone technique. Recall that if X is a partially ordered set and F X X is such that for x y e X x y implies F x F y then a mapping F is said to be non-decreasing. The main result of Agarwal et al. in