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The aim of this paper is to introduce a notion of  ϕ , F -contraction defined on a metric space with  w -distance. Moreover, fixed-point theorems are given in this framework. As an application, we prove the existence and uniqueness of a solution for the nonlinear Fredholm integral equations. Some illustrative examples are provided to advocate the usability of our results.

advances in mathematical physics

Fixed-Point Theorem for Nonlinear <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>F</mi> </math>-Contraction via <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mi>w</mi> </math>-Distance

Fixed-Point Theorem for Nonlinear F -Contraction via w -Distance

Fixed-Point Theorem for Nonlinear $F$ -Contraction via $w$ -Distance