Unification of the Fixed Point in Integral Type Metric Spaces

Panda Kumari,Nawab Hussain,Badriah Alamri,Sumit Chandok

doi:10.3390/sym10120732

Panda Kumari, Nawab Hussain + Show 2 more

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https://doi.org/10.3390/sym10120732

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Abstract

In metric fixed point theory, the conditions like “symmetry” and “triangle inequality” play a predominant role. In this paper, we introduce a new kind of metric space by using symmetry, triangle inequality, and other conditions like self-distances are zero. In this paper, we introduce the weaker forms of integral type metric spaces, thereby we establish the existence of unique fixed point theorems. As usual, illustrations and counter examples are provided wherever necessary.

Highlights

Introduction and PreliminariesSumati et al [1] introduced the weaker forms of various generating spaces and proved pertinent fixed point theorems
The study of fixed points satisfying cyclic mappings has been at the center of strong research activity in the last decade
We introduce some weaker forms of integral type metric spaces, that is the integral type metric space, the integral type dislocated metric space, and the integral type dislocated quasi-metric space

Summary

Introduction and Preliminaries

Sumati et al [1] introduced the weaker forms of various generating spaces and proved pertinent fixed point theorems. The study of fixed points satisfying cyclic mappings has been at the center of strong research activity in the last decade. In 1997, Chang et al [21] introduced the theory of a generating space of a quasi-metric family and established some interesting fixed point theorems. Symmetry 2018, 10, 732 general Caristi-type fixed point theorem for set-valued maps. Sumati et al [1] introduced weaker forms of various generating spaces and proved pertinent fixed point theorems. An integral type metric space ( X, dα ) is said to be complete if every Cauchy sequence in X converges to a point in X.

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