Abstract
In this work, we establish new fixed point theorems for w-generalized weak contraction mappings with respect to w-distances in complete metric spaces by using the concept of an altering distance function. As an application, we use the obtained results to aggregate the existence and uniqueness of the solution for nonlinear Fredholm integral equations and Volterra integral equations together with nonlinear fractional differential equations of Caputo type.
Highlights
In, the notion of an altering distance function was introduced and studied by Khan et al [ ], applying it to define weak contractions
We introduce the concept of a special w-distance, the so-called ceiling distance, and use this concept for proving fixed point theorems for generalized contraction mappings with respect to w-distances in complete metric spaces via the concept of an altering distance function
3 Main results we introduce the new concepts of a distance on a metric space and a generalized weak contraction mapping along with w-distance in metric spaces
Summary
In , the notion of an altering distance function was introduced and studied by Khan et al [ ], applying it to define weak contractions. They proved the existence and uniqueness of a fixed point for mappings satisfying such a contraction condition.
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