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Search Results (15)

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Keywords = Meir–Keeler contractions

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21 pages, 343 KiB  
Article
Fixed-Point Results for Krasnoselskii, Meir–Keeler, and Boyd–Wong-Type Mappings with Applications to Dynamic Market Equilibrium
by Lifang Guo, Rabia Bibi, Abeer Alshejari, Ekrem Savas, Tayyab Kamran and Umar Ishtiaq
Axioms 2024, 13(12), 867; https://doi.org/10.3390/axioms13120867 (registering DOI) - 12 Dec 2024
Viewed by 910
Abstract
This paper introduces the idea of a cone m-hemi metric space, which extends the idea of an m-hemi metric space. By presenting non-trivial examples, we demonstrate the superiority of cone m-hemi metric spaces over m-hemi metric spaces. Further, we [...] Read more.
This paper introduces the idea of a cone m-hemi metric space, which extends the idea of an m-hemi metric space. By presenting non-trivial examples, we demonstrate the superiority of cone m-hemi metric spaces over m-hemi metric spaces. Further, we extend the Banach contraction principle and Krasnoselskii, Meir–Keeler, Boyd–Wong, and some other fixed-point results in the setting of complete and compact cone m-hemi metric spaces. Furthermore, we provide several non-trivial examples and applications to the Fredholm integral equation and dynamic market equilibrium to demonstrate the validity of the main results. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory with Applications)
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17 pages, 311 KiB  
Article
Extension of Meir-Keeler-Khan (ψ − α) Type Contraction in Partial Metric Space
by Dimple Singh, Priya Goel, Ramandeep Behl and Iñigo Sarría
Axioms 2024, 13(9), 638; https://doi.org/10.3390/axioms13090638 - 18 Sep 2024
Cited by 1 | Viewed by 687
Abstract
In numerous scientific and engineering domains, fractional-order derivatives and integral operators are frequently used to represent many complex phenomena. They also have numerous practical applications in the area of fixed point iteration. In this article, we introduce the notion of generalized Meir-Keeler-Khan-Rational type [...] Read more.
In numerous scientific and engineering domains, fractional-order derivatives and integral operators are frequently used to represent many complex phenomena. They also have numerous practical applications in the area of fixed point iteration. In this article, we introduce the notion of generalized Meir-Keeler-Khan-Rational type (ψ−α)-contraction mapping and propose fixed point results in partial metric spaces. Our proposed results extend, unify, and generalize existing findings in the literature. In regards to applicability, we provide evidence for the existence of a solution for the fractional-order differential operator. In addition, the solution of the integral equation and its uniqueness are also discussed. Finally, we conclude that our results are superior and generalized as compared to the existing ones. Full article
(This article belongs to the Special Issue New Perspectives in Applied Mathematics with Nonlinear Equations and Dynamical Systems)
13 pages, 267 KiB  
Article
New Fixed Point Theorems for Generalized Meir–Keeler Type Nonlinear Mappings with Applications to Fixed Point Theory
by Shin-Yi Huang and Wei-Shih Du
Symmetry 2024, 16(8), 1088; https://doi.org/10.3390/sym16081088 - 22 Aug 2024
Cited by 2 | Viewed by 1386
Abstract
In this paper, we investigate new fixed point theorems for generalized Meir–Keeler type nonlinear mappings satisfying the condition (DH). As applications, we obtain many new fixed point theorems which generalize and improve several results available in the corresponding literature. An example is [...] Read more.
In this paper, we investigate new fixed point theorems for generalized Meir–Keeler type nonlinear mappings satisfying the condition (DH). As applications, we obtain many new fixed point theorems which generalize and improve several results available in the corresponding literature. An example is provided to illustrate and support our main results. Full article
(This article belongs to the Special Issue Fixed Point Theory and Its Applications Dedicated to the Memory of Professor William Arthur Kirk)
18 pages, 333 KiB  
Article
Meir–Keeler Fixed-Point Theorems in Tripled Fuzzy Metric Spaces
by Hui Yang
Mathematics 2023, 11(24), 4962; https://doi.org/10.3390/math11244962 - 14 Dec 2023
Cited by 2 | Viewed by 1555
Abstract
In this paper, we first propose the concept of a family of quasi-G-metric spaces corresponding to the tripled fuzzy metric spaces (or G-fuzzy metric spaces). Using their properties, we give the characterization of tripled fuzzy metrics. Second, we introduce the [...] Read more.
In this paper, we first propose the concept of a family of quasi-G-metric spaces corresponding to the tripled fuzzy metric spaces (or G-fuzzy metric spaces). Using their properties, we give the characterization of tripled fuzzy metrics. Second, we introduce the notion of generalized fuzzy Meir–Keeler-type contractions in G-fuzzy metric spaces. With the aid of the proposed notion, we show that every orbitally continuous generalized fuzzy Meir–Keeler-type contraction has a unique fixed point in complete G-fuzzy metric spaces. In the end, an example illustrates the validity of our results. Full article
14 pages, 331 KiB  
Article
(α − ψ) Meir–Keeler Contractions in Bipolar Metric Spaces
by Manoj Kumar, Pankaj Kumar, Rajagopalan Ramaswamy, Ola A. Ashour Abdelnaby, Amr Elsonbaty and Stojan Radenović
Mathematics 2023, 11(6), 1310; https://doi.org/10.3390/math11061310 - 8 Mar 2023
Cited by 3 | Viewed by 1670
Abstract
In this paper, we introduce the new notion of contravariant (α−ψ) Meir–Keeler contractive mappings by defining α-orbital admissible mappings and covariant Meir–Keeler contraction in bipolar metric spaces. We prove fixed point theorems for these contractions and also provide [...] Read more.
In this paper, we introduce the new notion of contravariant (α−ψ) Meir–Keeler contractive mappings by defining α-orbital admissible mappings and covariant Meir–Keeler contraction in bipolar metric spaces. We prove fixed point theorems for these contractions and also provide some corollaries of main results. An example is also be given in support of our main result. In the end, we also solve an integral equation using our result. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory and Its Applications)
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12 pages, 315 KiB  
Article
Common Fixed Point for Meir–Keeler Type Contraction in Bipolar Metric Space
by Penumarthy Parvateesam Murthy, Chandra Prakash Dhuri, Santosh Kumar, Rajagopalan Ramaswamy, Muhannad Abdullah Saud Alaskar and Stojan Radenovi’c
Fractal Fract. 2022, 6(11), 649; https://doi.org/10.3390/fractalfract6110649 - 4 Nov 2022
Cited by 8 | Viewed by 1453
Abstract
In mathematical analysis, the Hausdorff derivatives or the fractal derivatives play an important role. Fixed-point theorems and metric fixed-point theory have varied applications in establishing a unique common solution to differential equations and integral equations. In the present work, some fixed-point theorems using [...] Read more.
In mathematical analysis, the Hausdorff derivatives or the fractal derivatives play an important role. Fixed-point theorems and metric fixed-point theory have varied applications in establishing a unique common solution to differential equations and integral equations. In the present work, some fixed-point theorems using the extension of Meir–Keeler contraction in the setting of bipolar metric spaces have been proved. The derived results have been supplemented with non-trivial examples. Our results extend and generalise the results established in the past. We have provided an application to find an analytical solution to an Integral Equation to supplement the derived result. Full article
(This article belongs to the Special Issue New Trends on Fixed Point Theory)
14 pages, 297 KiB  
Article
Meir–Keeler Type Contraction in Orthogonal M-Metric Spaces
by Ateq Alsaadi, Bijender Singh, Vizender Singh and Izhar Uddin
Symmetry 2022, 14(9), 1856; https://doi.org/10.3390/sym14091856 - 6 Sep 2022
Cited by 8 | Viewed by 1728
Abstract
In this article, we prove fixed point results for a Meir–Keeler type contraction due to orthogonal M-metric spaces. The results of the paper improve and extend some recent developments in fixed point theory. The extension is assured by the concluding remarks and [...] Read more.
In this article, we prove fixed point results for a Meir–Keeler type contraction due to orthogonal M-metric spaces. The results of the paper improve and extend some recent developments in fixed point theory. The extension is assured by the concluding remarks and followed by the main theorem. Finally, an application of the main theorem is established in proving theorems for some integral equations and integral-type contractive conditions. Full article
(This article belongs to the Special Issue Elementary Fixed Point Theory and Common Fixed Points)
76 pages, 711 KiB  
Review
Fixed-Point Results for Meir–Keeler Type Contractions in Partial Metric Spaces: A Survey
by Erdal Karapınar, Ravi P. Agarwal, Seher Sultan Yeşilkaya and Chao Wang
Mathematics 2022, 10(17), 3109; https://doi.org/10.3390/math10173109 - 30 Aug 2022
Cited by 8 | Viewed by 2576
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Section C1: Difference and Differential Equations)
13 pages, 315 KiB  
Article
Interpolative Meir–Keeler Mappings in Modular Metric Spaces
by Erdal Karapınar, Andreea Fulga and Seher Sultan Yeşilkaya
Mathematics 2022, 10(16), 2986; https://doi.org/10.3390/math10162986 - 18 Aug 2022
Cited by 13 | Viewed by 1724
Abstract
Modular metric space is one of the most interesting spaces in the framework of the metric fixed point theory. The main goal of the paper is to provide some certain fixed point results in the context of modular metric spaces and non-Archimedean modular [...] Read more.
Modular metric space is one of the most interesting spaces in the framework of the metric fixed point theory. The main goal of the paper is to provide some certain fixed point results in the context of modular metric spaces and non-Archimedean modular metric spaces. In particular, we examine the existence of interpolative Meir–Keeler contraction types via admissible mappings for fixed point theory. Our results bring together several results available in the current corresponding literature. Full article
(This article belongs to the Special Issue New Progress in General Topology and Its Applications)
13 pages, 282 KiB  
Article
Multi-Step Inertial Hybrid and Shrinking Tseng’s Algorithm with Meir–Keeler Contractions for Variational Inclusion Problems
by Yuanheng Wang, Mingyue Yuan and Bingnan Jiang
Mathematics 2021, 9(13), 1548; https://doi.org/10.3390/math9131548 - 1 Jul 2021
Cited by 6 | Viewed by 2032
Abstract
In our paper, we propose two new iterative algorithms with Meir–Keeler contractions that are based on Tseng’s method, the multi-step inertial method, the hybrid projection method, and the shrinking projection method to solve a monotone variational inclusion problem in Hilbert spaces. The strong [...] Read more.
In our paper, we propose two new iterative algorithms with Meir–Keeler contractions that are based on Tseng’s method, the multi-step inertial method, the hybrid projection method, and the shrinking projection method to solve a monotone variational inclusion problem in Hilbert spaces. The strong convergence of the proposed iterative algorithms is proven. Using our results, we can solve convex minimization problems. Full article
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications)
20 pages, 309 KiB  
Article
Banach Contraction Principle and Meir–Keeler Type of Fixed Point Theorems for Pre-Metric Spaces
by Hsien-Chung Wu
Axioms 2021, 10(2), 57; https://doi.org/10.3390/axioms10020057 - 9 Apr 2021
Viewed by 3147
Abstract
The fixed point theorems in so-called pre-metric spaces is investigated in this paper. The main issue in the pre-metric space is that the symmetric condition is not assumed to be satisfied, which can result in four different forms of triangle inequalities. In this [...] Read more.
The fixed point theorems in so-called pre-metric spaces is investigated in this paper. The main issue in the pre-metric space is that the symmetric condition is not assumed to be satisfied, which can result in four different forms of triangle inequalities. In this case, the fixed point theorems in pre-metric space will have many different styles based on the different forms of triangle inequalities. Full article
(This article belongs to the Special Issue Theory and Application of Fixed Point)
17 pages, 292 KiB  
Article
On Some New Results in Graphical Rectangular b-Metric Spaces
by Pravin Baradol, Jelena Vujaković, Dhananjay Gopal and Stojan Radenović
Mathematics 2020, 8(4), 488; https://doi.org/10.3390/math8040488 - 1 Apr 2020
Cited by 8 | Viewed by 2420
Abstract
In this paper, we provide an approach to establish the Banach contraction principle (for the case λ ∈ [ 0 , 1 ) ) , Edelstein, Reich, and Meir–Keeler type contractions in the context of graphical rectangular b-metric space. The obtained results [...] Read more.
In this paper, we provide an approach to establish the Banach contraction principle (for the case λ ∈ [ 0 , 1 ) ) , Edelstein, Reich, and Meir–Keeler type contractions in the context of graphical rectangular b-metric space. The obtained results not only enrich and improve recent fixed point theorems of this new metric spaces but also provide positive answers to the questions raised by Mudasir Younis et al. (J. Fixed Point Theory Appl., doi:10.1007/s11784-019-0673-3, 2019). Full article
(This article belongs to the Special Issue Quantum Algebras and Operator Theory)
10 pages, 229 KiB  
Article
A Discussion on Random Meir-Keeler Contractions
by Cheng-Yen Li, Erdal Karapınar and Chi-Ming Chen
Mathematics 2020, 8(2), 245; https://doi.org/10.3390/math8020245 - 14 Feb 2020
Cited by 10 | Viewed by 1786
Abstract
The aim of this paper is to enrich random fixed point theory, which is one of the cornerstones of probabilistic functional analysis. In this paper, we introduce the notions of random, comparable MT- γ contraction and random, comparable Meir-Keeler contraction in the framework [...] Read more.
The aim of this paper is to enrich random fixed point theory, which is one of the cornerstones of probabilistic functional analysis. In this paper, we introduce the notions of random, comparable MT- γ contraction and random, comparable Meir-Keeler contraction in the framework of complete random metric spaces. We investigate the existence of a random fixed point for these contractions. We express illustrative examples to support the presented results. Full article
(This article belongs to the Section C2: Dynamical Systems)
10 pages, 269 KiB  
Article
Results in wt-Distance over b-Metric Spaces
by Erdal Karapınar and Cristian Chifu
Mathematics 2020, 8(2), 220; https://doi.org/10.3390/math8020220 - 9 Feb 2020
Cited by 36 | Viewed by 2696
Abstract
In this manuscript, we introduce Meir-Keeler type contractions and Geraghty type contractions in the setting of the w t -distances over b-metric spaces. We examine the existence of a fixed point for such mappings. Under some additional assumption, we proved the uniqueness [...] Read more.
In this manuscript, we introduce Meir-Keeler type contractions and Geraghty type contractions in the setting of the w t -distances over b-metric spaces. We examine the existence of a fixed point for such mappings. Under some additional assumption, we proved the uniqueness of the found fixed point. Full article
(This article belongs to the Special Issue Nonlinear Optimization, Variational Inequalities and Equilibrium Problems)
11 pages, 246 KiB  
Article
Best Proximity Point Theorems for Two Weak Cyclic Contractions on Metric-Like Spaces
by Erdal Karapınar, Chi-Ming Chen and Chih-Te Lee
Mathematics 2019, 7(4), 349; https://doi.org/10.3390/math7040349 - 14 Apr 2019
Cited by 12 | Viewed by 3204
Abstract
In this paper, we establish two best proximity point theorems in the setting of metric-like spaces that are based on cyclic contraction: Meir–Keeler–Kannan type cyclic contractions and a generalized Ćirić type cyclic φ -contraction via the MT -function. We express some examples to [...] Read more.
In this paper, we establish two best proximity point theorems in the setting of metric-like spaces that are based on cyclic contraction: Meir–Keeler–Kannan type cyclic contractions and a generalized Ćirić type cyclic φ -contraction via the MT -function. We express some examples to indicate the validity of the presented results. Our results unify and generalize a number of best proximity point results on the topic in the corresponding recent literature. Full article
(This article belongs to the Special Issue Recent Advances in Fixed Point and Best Proximity Point Problems and Their Applications)
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