Abstract
The solutions for many real life problems may be obtained by interpreting the given problem mathematically in the form f ( x ) = x . One such example is that of the famous Borsuk–Ulam theorem in which, using some fixed point argument, it can be guaranteed that at any given time we can find two diametrically opposite places in a planet with same temperature. Thus, the correlation of symmetry is inherent in the study of fixed point theory. In this article, some new results concerning coincidence and a common fixed point for an A φ -contraction and a generalized ϕ -type weak contraction are established. We prove our results for set valued maps without using continuity of the corresponding maps and completeness of the relevant space. Our results generalize and extend several existing results. Some new examples are given to demonstrate the generality and non-triviality of our results.
Highlights
The Banach fixed point theorem is considered the most versatile work in fixed point theory.The study of similar results in nonlinear contraction maps was initiated by Boyd and Wong [1].Fixed points for set valued mappings play a fundamental role in nonlinear analysis
Fixed points of multivalued operators are important for studies in set valued analysis
After the Introduction part, this paper is divided into four sections: (a) Preliminaries: here we recall the definitions and existing results that are essential for our work; (b) Main Results: we introduce A φ -contraction and generalized φ-type weak contraction for set valued maps and prove our new results; (c) Discussion: here, we discuss the results and how they can be interpreted from the perspective of previous studies and of the working hypotheses
Summary
The Banach fixed point theorem is considered the most versatile work in fixed point theory.The study of similar results in nonlinear contraction maps was initiated by Boyd and Wong [1].Fixed points for set valued mappings play a fundamental role in nonlinear analysis. Fixed points of multivalued operators are important for studies in set valued analysis. Results in this direction were given by Markin [2] and Nadler [3]. Afterwards, many generalizations of Nadler’s result were obtained in various directions In this context, the reference of set valued and multivalued contraction carried out by Assad and Kirk [4] can be estimated. The reference of set valued and multivalued contraction carried out by Assad and Kirk [4] can be estimated They proved a result for set valued maps defined on a complete metric space by considering another assumption that the space is metrically convex
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
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.
