Meir-Keeler Contraction In Rectangular<i>M</i>−Metric Space

Asim, Mohammad; Mujahid, Samad; Uddin, Izhar

doi:10.1515/taa-2021-0106

Cited by 4 publications

(1 citation statement)

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“…In the literature, there are two ways to generalized the Banach contraction principle either change the contraction condition or alter the metric space. In fixed point theory several contractions defined in metric space such that Boyd and Wong's nonlinear contraction principle [11], Meir-Keeler contraction [20,1,6], Suzuki contraction [33], Kannan contraction [17], Ćirić generalized contraction [14], Ćirić's quasi contraction [15], weak-contraction [29], Chatterjea contraction [13], Zamfirescu contraction [35] and F -Suzuki contraction [27] and many more [9,25]. In 2012, Wardowski [34] introduced a new type of contraction for real-valued mapping F defined on positive real numbers and satisfying some conditions and obtained a fixed point theorem for it.…”

Section: Introductionmentioning

confidence: 99%

Fixed point theorems for F- contraction mapping in complete rectangular M-metric space

2022

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Section: Introductionmentioning

confidence: 99%

Fixed point theorems for F- contraction mapping in complete rectangular M-metric space

2022

Self Cite

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Fixed-Point Results for Meir–Keeler Type Contractions in Partial Metric Spaces: A Survey

et al. 2022

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In this paper, we aim to review Meir–Keeler contraction mappings results on various abstract spaces, in particular, on partial metric spaces, dislocated (metric-like) spaces, and M-metric spaces. We collect all significant results in this direction by involving interesting examples. One of the main reasons for this work is to help young researchers by giving a framework for Meir Keeler’s contraction.

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New fixed point results in double controlled metric type spaces with applications

Azmi

2023

MATH

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<abstract><p>The concept of an $ { \mathcal F} $-contraction was introduced by Wardowski, while Samet et al. introduced the class of $ \alpha $-admissible mappings and the concept of ($ \alpha $-$ \psi $)-contractive mapping on complete metric spaces. In this paper, we study and extend two types of contraction mappings: ($ \alpha $-$ \psi $)-contraction mapping and ($ \alpha $-$ { \mathcal F} $)-contraction mapping, and establish new fixed point results on double controlled metric type spaces. Moreover, we demonstrate some examples and present an application of our result on the existence and uniqueness of the solution for an integral equation.</p></abstract>

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Meir-Keeler Contraction In RectangularM−Metric Space

Abstract: In this paper, we prove some fixed point theorems for a Meir-Keeler type Contraction in rectangular M−metric space. Thus, our results extend and improve very recent results in fixed point theory.

Cited by 4 publications

References 28 publications

Fixed point theorems for F- contraction mapping in complete rectangular M-metric space

Fixed point theorems for F- contraction mapping in complete rectangular M-metric space

Fixed-Point Results for Meir–Keeler Type Contractions in Partial Metric Spaces: A Survey

New fixed point results in double controlled metric type spaces with applications

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