Solvability of integral equations through fixed point theorems: a survey

Abstract

This paper surveys regarding solutions of linear and nonlinear integral equations through fixed point theorem. Banach's contraction mapping principle is the most widely applied fixed point theorem in all of analysis with special applications to the theory of integral equations. Over a decade researchers have generalized the definition of a metric space and using the technique of fixed point have found solutions to many linear and nonlinear Volterra-Fredholm integral equations.

Keywords

• fixed point
• b-metric spaces
• extended b-metric spaces
• dislocated extended b-metric space
• rational weak f-contraction
• metric space