Abstract
Abstract In this article, we prove some existence and uniqueness results on coincidence points for g-increasing mappings satisfying generalized φ-contractivity conditions in ordered metric spaces. As an application of one of our newly proved results, we indicate the formulation of a coupled coincidence theorem. Our results generalize, extend, modify, improve, sharpen, enrich, and complement several well-known results of the existing literature. Also, we point out that a recent coincidence point result proved in Dalal et al. (J. Adv. Math. 7(1):1084-1094, 2014) contains errors and omissions. MSC:47H10, 54H25.
Highlights
In, Ran and Reurings [ ] extended the Banach contraction principle in ordered metric spaces for continuous monotone mappings with some applications to matrix equations wherein the involved contractive condition is required to hold merely on elements which are comparable in the underlying partial ordering
Nieto and RodríguezLópez [ ] analogously proved a fixed point theorem for a decreasing mapping in ordered metric space and gave some applications of their results to ordinary differential equations
The idea of the coupled fixed point was initiated by Guo and Lakshmikantham [ ] in, which was well followed by Bhaskar and Lakshmikantham [ ] where the authors introduced the notion of mixed monotone property for a linear contraction F : X → X and utilized the same to prove some theorems on the existence and uniqueness of coupled fixed points, which can be viewed as a coupled formulation of certain results of Nieto and Rodríguez-López [ ]
Summary
In , Ran and Reurings [ ] extended the Banach contraction principle in ordered metric spaces for continuous monotone mappings with some applications to matrix equations wherein the involved contractive condition is required to hold merely on elements which are comparable in the underlying partial ordering.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
