Abstract
In this paper, we introduce a new class of generalized weakly contractive mappings and prove common fixed point results by using different algorithms involving this new class of mappings in the framework ofb-metric spaces, which generalize the results of Cho. We also provide two examples to show the applicability and validity of our results. As an application of our result, we obtain a solution to an integral equation. Our results extend and improve several comparable results in the existing literature.
Highlights
The Banach fixed point theorem [1] popularly known as the Banach contraction mapping principle is a rewarding result in fixed point theory
Some authors have researched on the fixed point theorems of various new types of contractive conditions in b-metric space
If T is a generalized weakly contractive mapping, there exists a unique z ∈ X such that z = Tz and φðzÞ = 0: Motivated and inspired by Theorem 2.1 in [44], in this paper, our purpose is to introduce a new class of generalized weakly contractive mappings and obtain a few of common fixed point results by using different algorithms involving generalized weakly contractive conditions in the framework of b-metric space, which generalize the results of Cho
Summary
The Banach fixed point theorem [1] popularly known as the Banach contraction mapping principle is a rewarding result in fixed point theory. Choudhury et al [36] obtained a generalization of the weak contraction principle in metric spaces by using altering distance functions as follows: Theorem 1 (see [36]). If T is a generalized weakly contractive mapping, there exists a unique z ∈ X such that z = Tz and φðzÞ = 0: Motivated and inspired by Theorem 2.1 in [44], in this paper, our purpose is to introduce a new class of generalized weakly contractive mappings and obtain a few of common fixed point results by using different algorithms involving generalized weakly contractive conditions in the framework of b-metric space, which generalize the results of Cho. we provide examples that elaborated the useability of our results. We present an application to the existence of solutions to an integral equation by means of one of our results
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