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The purpose of this work is to introduce the new contractive condition which involves mw-distances in metric spaces. The fixed point theorems for mappings satisfying such contractive condition are established via the idea of an adapting-ceiling distance. Two illustrative examples are also given to confirm that our results rightly generalize many results in the literatures. As an application, the existence and uniqueness of the solution for nonlinear Fredholm integral equations and nonlinear Volterra integral equations are investigated via our main result. [ABSTRACT FROM AUTHOR]

The purpose of this work is to establish new fixed point theorems for generalized contraction mappings with respect to w-distances in complete metric spaces by using the concept of a weak altering distance function. Two illustrative examples are provided to advocate the usability of our results. Also, we present a numerical experiment for approximating a fixed point in these examples. As an application, the received results are used to summarize the existence and uniqueness of the solution for nonlinear Fredholm integral equations. [ABSTRACT FROM AUTHOR]

The aim of this work is to establish a new fixed point theorem for generalized contraction mappings with respect to w-distances in complete metric spaces. An illustrative example is provided to advocate the usability of our results. Also, we give a numerical experiment for approximating a fixed point in these examples. As an application, the received results are used to summarize the existence and uniqueness of the solution for nonlinear integral equations and nonlinear fractional differential equations of Caputo type. [ABSTRACT FROM AUTHOR]