Abstract
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.
Highlights
Introduction and preliminaries TheBanach contraction mapping plays an important role in solving nonlinear problems
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
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
Summary
≥ (1 − |λ| M2) x − y , since condition (4.3) implies that |λ| M2 < 1, So (4.7) yields x−y ≤. There exists 0 ≤ m < 1 depending of x and y such that m(x, y) T x − T y ≤ Sx − Sy ≤ T x − T y. By (iii), φ is a non-negative, continuous, 2-superadditive and G-positive homogeneous functional on the cone R+ satisfying (2.2). For u = Sx − Sy , v = T x − T y and the inequality (4.9), the Lemma 4.1 allows us to conclude that,.
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