Abstract
Abstract The purpose of this paper is to study behavior of a rational type contraction introduced in [A fixed point theorem for contractions of rational type in partially ordered metric spaces, Ann. Univ. Ferrara, 2013, 59, 251–258] in context of ordered dualistic partial metric spaces and to investigate sufficient conditions for the existence of a fixed point in this space. These results extend various comparable results, existing in the literature. We give examples to explain our findings. We apply our result to prove the existence of the solution of functional equation.
Highlights
The generalization of a metric function has been done by a number of researchers
The purpose of this paper is to study behavior of a rational type contraction introduced in [A xed point theorem for contractions of rational type in partially ordered metric spaces, Ann
For the current paper we describe partial metric and dualistic partial metric in detail
Summary
The generalization of a metric function has been done by a number of researchers (see [1,2,3,4,5]) The latest in this regard is introduced by Jleli and Samet [6]. Matthews called new metric function with non-zero self-distance a partial metric He applied this function as a suitable mathematical tool for program veri cation and generalized Banach Contraction Principle. This led a number of researchers to investigate existence of xed points, common xed points and coupled xed points of self-mappings de ned on a partial metric space (see [7,8,9,10] and references ). Many authors have investigated xed points of contractions of rational type and contractive mappings in metric and partial metric spaces, for details, see [15,16,17,18,19,20,21,22,23,24,25,26,27]
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.
