Fixed Point Results for φ − (γ, η, n, m)−Contractions with Applications to Nonlinear Integral Equations

The aim of this paper is to introduce a new class of pair of contraction mappings, called φ - (γ, η, n, m)-contraction pairs, and obtain common fixed point theorems for a pair of mappings in this class, satisfying a weakly compatible condition. As an application, we use mappings of this class to find the existence of solutions for nonlinear integral equations on the space of continuous functions and in some of its subspaces. Moreover, some examples are given here to illustrate the applicability of these results.