Abstract
This article presents the E -parametric metric space, which is a generalized concept of parametric metric space. After that, the discussion is concerned with the existence of fixed points of single and multivalued maps on E -parametric metric spaces satisfying some contractive inequalities defined by an auxiliary function.
Highlights
Introduction and PreliminariesMetric fixed point theory is a very fruitful area of research belonging to nonlinear analysis and operator theory
This article presents fixed point theorems for mappings satisfying the contraction type conditions defined with auxiliary functions over E-parametric metric spaces
The readers will get many fixed point results as the outcome of this work. These results have been obtained in the following ways: (1) Defining an auxiliary function through a particular form
Summary
Metric fixed point theory is a very fruitful area of research belonging to nonlinear analysis and operator theory. A map Pm : H × H × ð0,∞Þ ⟶ 1⁄20,∞Þ (where H ≠ ∅) is said to be a parametric metric on H if it satisfies the following axioms:. Khalehoghli et al [10] took a binary relation E on H and a simple metric d on H to define an R-metric space, denoted as ðH, d, BRÞ They said that a self map T on H is a BR -contraction, if. D Tl, Tl′ ≤ kd l, l′ , ð1Þ for all l,l′ ∈ H with lBRl′, where 0 < k < 1 Along with this definition, the authors defined the concepts of BR-continuity and BR-preserving property in order to extend the result of Banach on R-metric spaces
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.
