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

Abstract

In this paper, we prove fixed point theorem via orthogonal Geraghty type α-admissible contraction map in an orthogonal complete Branciari b-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.

Keywords

• orthogonal set
• orthogonal preserving
• orthogonal continuous
• orthogonal Branciari <i>b</i>-metric space
• orthogonal Geraghty type <i>α</i>-admissible contraction
• fixed point theory