Abstract
AbstractIn this paper, we introduce the notion of cyclic R-contraction mapping and then study the existence of fixed points for such mappings in the framework of metric spaces. Examples and application are presented to support the main result. Our result unify, complement, and generalize various comparable results in the existing literature.
Highlights
Introduction and preliminariesLet (X, d) be any metric space, Y a subset of X, and f : X → Y
Fixed point theory plays a vital role in the study of existence of solutions of nonlinear problems arising in physical, biological, and social sciences
Some fixed point results ensure the existence of a solution but provide no information about the uniqueness and determination of the solution
Summary
A mapping ζ : [ , ∞) × [ , ∞) → R is called a simulation function if the following conditions hold:. Rodan-Lopez-de-Hierro and Shahzad [ ] considered the following condition: ( ) If {an} and {bn} are sequences in ( , ∞) ∩ A such that limn→∞ bn = and (an, bn) >. A self-map f of X is called an R-contraction if there exists ∈ RA such that ran(d) ⊆ A and (d(fx, fy), d(x, y)) > for all x, y ∈ X with x = y, where RA is the family of all functions : A × A → R satisfying the conditions ( ) and ( ), and ran(d) is the range of the metric d defined by ran(d) = {d(x, y) : x, y ∈ X} ⊆ [ , ∞).
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.
