Integral Equation via Fixed Point Theorems on a New Type of Convex Contraction in <i>b</i>-Metric and 2-Metric Spaces

Abstract

Our paper is devoted to describing a new way of generalized convex contraction of type-2 in the framework of b-metric spaces and 2-metric spaces. First, the concept of a new generalized convex contraction on b-metric spaces and 2-metric spaces is introduced, and fixed point theorem is extended to these spaces. Some examples supporting our main results are also presented. Finally, we apply our main result to approximating the solution of the Fredholm integral equation.

Keywords

• fixed point approximation
• fixed point
• new convex contraction
• b-metric
• α-admissible
• 2-metric spaces