Solution to Integral Equation in an <i>O</i>-Complete Branciari <i>b</i>-Metric Spaces

Solution to Integral Equation in an <i>O</i>-Complete Branciari <i>b</i>-Metric Spaces

In this paper, we prove fixed point theorem via orthogonal Geraghty type <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-admissible contract...

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Bibliographic Details
Main Authors: Menaha Dhanraj, Arul Joseph Gnanaprakasam, Gunaseelan Mani, Ozgur Ege, Manuel De la Sen
Format: Article
Language:English
Published: MDPI AG 2022-12-01
Series:Axioms
Subjects:
orthogonal set
orthogonal preserving
orthogonal continuous
orthogonal Branciari <i>b</i>-metric space
orthogonal Geraghty type <i>α</i>-admissible contraction
fixed point theory
Online Access:https://www.mdpi.com/2075-1680/11/12/728
Description
Summary:In this paper, we prove fixed point theorem via orthogonal Geraghty type <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-admissible contraction map in an orthogonal complete Branciari <i>b</i>-metric spaces context. An example is presented to strengthen our main result. We provided an application to find the existence and uniqueness of a solution to the Volterra integral equation. We have compared the approximate solution and exact solution numerically.
ISSN:2075-1680

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