Abstract
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.
Highlights
1 Introduction The most well-known fixed point result in the metrical fixed point theory is Banach’s contraction mapping principle. Since this principle requires only the structure of a complete metric space with contractive condition on the mapping, which is easy to test in this setting, it is the most widely applied fixed point result in many branches of mathematics
Some fixed point results for generalized contraction mappings have been proved by Ri [3] as follows: Aydi et al Advances in Difference Equations (2018) 2018:132
Based on the above mentioned fact, we present new fixed point theorems for generalized contraction mappings with respect to w-distances in complete metric spaces, which is an extension of Ri’s fixed point result, and give an example for showing the usability of our results while Theorem 1.1 is not applicable
Summary
The most well-known fixed point result in the metrical fixed point theory is Banach’s contraction mapping principle. Some fixed point results for generalized contraction mappings have been proved by Ri [3] as follows: Aydi et al Advances in Difference Equations (2018) 2018:132
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