On Some Common Fixed Point Results for Weakly Contraction Mappings with Application

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 of b -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.

A new fixed point result in bipolar controlled fuzzy metric spaces with application

“…Gravity, ground vibrations, earthquakes, tension force, and other external forces may work on the system. The critically damped motion of this system subjected to the external force F is governed by the following initial value problem, Let m be the mass of the spring and F be the external force acting on it [14].…”

Some New Types of α_(β^(-1) )-admissible Mappings and Fixed Point Results

“…Li. and Guan [5] introduced 𝛼 𝑠 𝑝 and 𝜌 − 𝛼 𝑠 𝑝 admissible condition in b-metric space. Likewise, Hussain et al [6] introduced 𝛼 -admissible mapping with respect to 𝜂 .…”

“…As we motivated and inspired by the papers [2], [3], [4], [5] and [7], our aim is to introduce 𝛼 𝛽 −1admissible mapping to prove some fixed point theorems by using 𝛼 − 𝜑 contraction in complete Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 3s (2024) 368 https://internationalpubls.com metric spaces in this paper.…”

Common Fixed Point Theorems for Weakly Contractions in Rectangular b -Metric Spaces with Supportive Applications

“…Hao and Guan [35] proved common fixed point result dealing with a new class of generalized weakly contraction conditions in complete b-metric spaces as follows.…”