Abstract
We establish coincidence and fixed point theorems for mappings satisfying generalized weakly contractive conditions on the setting of ordered gauge spaces. Presented theorems extend and generalize many existing studies in the literature. We apply our obtained results to the study of existence and uniqueness of solutions to some classes of nonlinear integral equations.
Highlights
1 Introduction Fixed point theory is considered as one of the most important tools of nonlinear analysis that widely applied to optimization, computational algorithms, physics, variational inequalities, ordinary differential equations, integral equations, matrix equations and so on
The Banach contraction principle [7] is a fundamental result in fixed point theory
Theorem 1.10 (Harjani and Sadarangani [3]) Let (X, ≼) be a partially ordered set and suppose that there exists a metric d in X such that (X, d) is a complete metric space
Summary
Fixed point theory is considered as one of the most important tools of nonlinear analysis that widely applied to optimization, computational algorithms, physics, variational inequalities, ordinary differential equations, integral equations, matrix equations and so on (see, for example, [1,2,3,4,5,6]). Theorem 1.5 (Dutta and Choudhury [20]) Let (X, d) be a complete metric space and T : X ® X be a mapping satisfying ψ(d(Tx, Ty)) ≤ ψ(d(x, y)) − φ(d(x, y)), for all x, y Î X, where ψ and are altering distance functions.
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