Abstract
We introduce the notion of a parametricS-metric space as generalization of a parametric metric space. Using some expansive mappings, we prove a fixed-point theorem on a parametricS-metric space. It is important to obtain new fixed-point theorems on a parametricS-metric space because there exist some parametricS-metrics which are not generated by any parametric metric. We expect that many mathematicians will study various fixed-point theorems using new expansive mappings (or contractive mappings) in a parametricS-metric space.
Highlights
Introduction and BackgroundsContractive conditions have been started by studying Banach’s contraction principle
Some fixed-point theorems have been still investigated using the notions of a parametric metric space and a parametric b-metric space for various contractive or expansive mappings
Hussain et al proved some fixed-point theorems on complete parametric metric spaces and triangular intuitionistic fuzzy metric spaces [7]
Summary
Contractive conditions have been started by studying Banach’s contraction principle These conditions have been used in various fixed-point theorems for some generalized metric spaces. The concept of a parametric b-metric space as generalization of a parametric metric space was given. Some fixed-point theorems have been still investigated using the notions of a parametric metric space and a parametric b-metric space for various contractive or expansive mappings (see [7,8,9,10] for more details). Hussain et al proved some fixed-point theorems on complete parametric metric spaces and triangular intuitionistic fuzzy metric spaces [7]. We prove some fixed-point results under various expansive mappings in a parametric S-metric space.
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