Generalized contraction mappings of rational type and applications to nonlinear integral equations

Abstract

The aim of the present paper is to introduce a new class of pair of contraction mappings, called ψ − (α, β, m)-contraction pairs, and obtain common fixed point theorems for a pair of mappings in this class, satisfying a minimal commutativity condition. Afterwards, we will use mappings in this class to analyze the existence of solutions for a class of nonlinear integral equations on the space of con- tinuous functions and in some of its subspaces. Concrete examples are also provided in order to illustrate the applicability of the results.

Keywords

• common fixed point
• altering distance
• integral equation
• weakly compatible mappings