Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (50)

Search Parameters:
Keywords = Ćirić-type contraction

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
26 pages, 378 KiB  
Article
Existence and Uniqueness Results for Fuzzy Bipolar Metric Spaces
by Umar Ishtiaq, Fahad Jahangeer, Mubariz Garayev and Ioan-Lucian Popa
Symmetry 2025, 17(2), 180; https://doi.org/10.3390/sym17020180 - 24 Jan 2025
Viewed by 515
Abstract
In this paper, we present the concept of (Υ,Ω)-iterativemappings in the setting of fuzzy bipolar metric space. The symmetric property in fuzzy bipolar metric spaces guarantees that the distance between any two elements remains invariant under permutation, ensuring [...] Read more.
In this paper, we present the concept of (Υ,Ω)-iterativemappings in the setting of fuzzy bipolar metric space. The symmetric property in fuzzy bipolar metric spaces guarantees that the distance between any two elements remains invariant under permutation, ensuring consistency and uniformity in measurement regardless of the order in which the elements are considered. Furthermore, we prove several best proximity point results by utilizing (Υ,Ω)-fuzzy bipolar proximal contraction, (Υ,Ω)-Reich–Rus–Ciric type proximal contraction, (Υ,Ω)-Kannan type proximal contraction and (Υ,Ω)-Hardy–Rogers type contraction. Furthermore, we provide some non-trivial examples to show the comparison with the existing results in the literature. At the end, we present an application to find the existence and uniqueness of a solution of an integral equation by applying the main result. Full article
Show Figures

Figure 1

15 pages, 328 KiB  
Article
Partial Metrics Viewed as w-Distances: Extending Some Powerful Fixed-Point Theorems
by Salvador Romaguera and Pedro Tirado
Mathematics 2024, 12(24), 3991; https://doi.org/10.3390/math12243991 - 18 Dec 2024
Viewed by 643
Abstract
Involving w-distances and hybrid contractions that combine conditions of the Ćirić type and Samet et al. type, we obtain some general fixed-point results for quasi-metric spaces from which powerful and significant fixed-point theorems on partial metric spaces are deduced as special cases. [...] Read more.
Involving w-distances and hybrid contractions that combine conditions of the Ćirić type and Samet et al. type, we obtain some general fixed-point results for quasi-metric spaces from which powerful and significant fixed-point theorems on partial metric spaces are deduced as special cases. We present examples showing that our results are real generalizations of those corresponding to the partial metric case and we give an application to the study of recursive equations where the usual Baire partial metric on a domain of words is replaced with a suitable w-distance. Our approach is inspired on the nice fact, stated by Matthews, that every partial metric induces a weighted quasi-metric. Then, we define the notion of a strong w-distance and deduce that every partial metric is a symmetric strong w-distance for its induced weighted quasi-metric space. Full article
(This article belongs to the Special Issue Novel Approaches in Fuzzy Sets and Metric Spaces)
20 pages, 321 KiB  
Article
Some Innovative Results for Interpolative Reich–Rus–Ćirić-Type Contractions in Rectangular m-Metric Spaces
by Muhammad Zahid, Ali Raza and Safeer Hussain Khan
Axioms 2024, 13(12), 829; https://doi.org/10.3390/axioms13120829 - 27 Nov 2024
Viewed by 701
Abstract
In this paper, we study the existence of fixed points for interpolative Reich–Rus–Ćirić-type contractions in the setting of rectangular m-metric spaces. The use of the rectangular inequality, in place of the conventional triangle inequality, introduces a higher level of complexity in the [...] Read more.
In this paper, we study the existence of fixed points for interpolative Reich–Rus–Ćirić-type contractions in the setting of rectangular m-metric spaces. The use of the rectangular inequality, in place of the conventional triangle inequality, introduces a higher level of complexity in the computations, requiring more careful and refined analysis. We consider two distinct cases based on the sum of the interpolative exponents: one where the sum is less than 1, and another where the sum exceeds 1. The results we present generalize several existing theorems in the literature, and each is supplemented with illustrative examples to demonstrate their applicability. Moreover, we deduce corresponding results on m-metric spaces from these results, which are new themselves. They are also validated through examples. Full article
18 pages, 348 KiB  
Article
Approximating Fixed Points via Hybrid Enriched Contractions in Convex Metric Space with an Application
by Bhumika Rani, Jatinderdeep Kaur and Satvinder Singh Bhatia
Axioms 2024, 13(12), 815; https://doi.org/10.3390/axioms13120815 - 22 Nov 2024
Cited by 1 | Viewed by 736
Abstract
In the present study, we define hybrid enriched contractions of the Hardy–Rogers type and of the Ćirić–Reich–Rus type in the framework of convex metric space. We demonstrate the presence and the approximation of fixed points for contraction mappings by using Krasnoselskij iteration. The [...] Read more.
In the present study, we define hybrid enriched contractions of the Hardy–Rogers type and of the Ćirić–Reich–Rus type in the framework of convex metric space. We demonstrate the presence and the approximation of fixed points for contraction mappings by using Krasnoselskij iteration. The main conclusions of this study are shown to be corollaries or implications of multiple important fixed point theory findings. Some examples have also been provided to show the validity of our results. Towards the end of this paper, we study the solution of the nonlinear equations as an application of our main results. Full article
Show Figures

Figure 1

17 pages, 312 KiB  
Article
Stability of Fixed Points of Partial Contractivities and Fractal Surfaces
by María A. Navascués
Axioms 2024, 13(7), 474; https://doi.org/10.3390/axioms13070474 - 13 Jul 2024
Cited by 2 | Viewed by 955
Abstract
In this paper, a large class of contractions is studied that contains Banach and Matkowski maps as particular cases. Sufficient conditions for the existence of fixed points are proposed in the framework of b-metric spaces. The convergence and stability of the Picard iterations [...] Read more.
In this paper, a large class of contractions is studied that contains Banach and Matkowski maps as particular cases. Sufficient conditions for the existence of fixed points are proposed in the framework of b-metric spaces. The convergence and stability of the Picard iterations are analyzed, giving error estimates for the fixed-point approximation. Afterwards, the iteration proposed by Kirk in 1971 is considered, studying its convergence, stability, and error estimates in the context of a quasi-normed space. The properties proved can be applied to other types of contractions, since the self-maps defined contain many others as particular cases. For instance, if the underlying set is a metric space, the contractions of type Kannan, Chatterjea, Zamfirescu, Ćirić, and Reich are included in the class of contractivities studied in this paper. These findings are applied to the construction of fractal surfaces on Banach algebras, and the definition of two-variable frames composed of fractal mappings with values in abstract Hilbert spaces. Full article
(This article belongs to the Special Issue Trends in Fixed Point Theory and Fractional Calculus)
12 pages, 275 KiB  
Article
Suzuki–Ćirić-Type Nonlinear Contractions Employing a Locally ζ-Transitive Binary Relation with Applications to Boundary Value Problems
by Doaa Filali and Faizan Ahmad Khan
Mathematics 2024, 12(13), 2058; https://doi.org/10.3390/math12132058 - 30 Jun 2024
Viewed by 1084
Abstract
This article is devoted to enhancing a class of generalized Suzuki-type nonlinear contractions following Pant to a class of Suzuki–Ćirić-type nonlinear contractions via comparison functions via a locally ζ-transitive relation and implemented the same to ascertain certain fixed-point results. The outcomes presented [...] Read more.
This article is devoted to enhancing a class of generalized Suzuki-type nonlinear contractions following Pant to a class of Suzuki–Ćirić-type nonlinear contractions via comparison functions via a locally ζ-transitive relation and implemented the same to ascertain certain fixed-point results. The outcomes presented herewith unify and generalize a few existing findings. An illustrative examples is offered to explain our findings. Our outcomes assist us in figuring out the unique solution to a boundary value problem. Full article
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications II)
13 pages, 305 KiB  
Article
On Prešić-Type Mappings: Survey
by Youssef Achtoun, Milanka Gardasević-Filipović, Slobodanka Mitrović and Stojan Radenović
Symmetry 2024, 16(4), 415; https://doi.org/10.3390/sym16040415 - 2 Apr 2024
Cited by 2 | Viewed by 1100
Abstract
This paper is dedicated to the memory of the esteemed Serbian mathematician Slaviša B. Prešić (1933–2008). The primary aim of this survey paper is to compile articles on Prešić-type mappings published since 1965. Additionally, it introduces a novel class of symmetric contractions known [...] Read more.
This paper is dedicated to the memory of the esteemed Serbian mathematician Slaviša B. Prešić (1933–2008). The primary aim of this survey paper is to compile articles on Prešić-type mappings published since 1965. Additionally, it introduces a novel class of symmetric contractions known as Prešić–Menger and Prešić–Ćirić–Menger contractions, thereby enriching the literature on Prešić-type mappings. The paper endeavors to furnish young researchers with a comprehensive resource in functional and nonlinear analysis. The relevance of Prešić’s method, which generalizes Banach’s theorem from 1922, remains significant in metric fixed point theory, as evidenced by recent publications. The overview article addresses the growing importance of Prešić’s approach, coupled with new ideas, reflecting the ongoing advancements in the field. Additionally, the paper establishes the existence and uniqueness of fixed points in Menger spaces, contributing to the filling of gaps in the existing literature on Prešić’s works while providing valuable insights into this specialized domain. Full article
(This article belongs to the Special Issue New Trends in Fixed Point Theory with Emphasis on Symmetry)
18 pages, 315 KiB  
Article
On Generalized Sehgal–Guseman-Like Contractions and Their Fixed-Point Results with Applications to Nonlinear Fractional Differential Equations and Boundary Value Problems for Homogeneous Transverse Bars
by Muhammad Din, Umar Ishtiaq, Muzammil Mukhtar, Salvatore Sessa and Hassan Ali Ghazwani
Mathematics 2024, 12(4), 541; https://doi.org/10.3390/math12040541 - 8 Feb 2024
Cited by 3 | Viewed by 1278
Abstract
The goal of this study is to describe the class of modified Sehgal–Guseman-like contraction mappings and set up some fixed-point results in S-metric spaces. The class of generalized Sehgal–Guseman-like contraction mappings contains enhancements of Banach contractions, Kannan contractions, Chatterjee contractions, Chatterjee-type contractions, [...] Read more.
The goal of this study is to describe the class of modified Sehgal–Guseman-like contraction mappings and set up some fixed-point results in S-metric spaces. The class of generalized Sehgal–Guseman-like contraction mappings contains enhancements of Banach contractions, Kannan contractions, Chatterjee contractions, Chatterjee-type contractions, quasi-contractions, Ćirić–Reich–Rus-type contractions, Hardy–Rogers-type contractions, Reich-type contractions, interpolative Kannan contractions, interpolative Chatterjee contractions, among others, with their generalizations in S-metric spaces. We offer significant examples to substantiate the reliability of our results. This study also establishes consequential fixed-point results and applies them to nonlinear fractional differential equations and the boundary value problem for homogeneous transverse bars. At the end of the manuscript, we present an important open problem. Full article
18 pages, 336 KiB  
Article
Certain Interpolative Proximal Contractions, Best Proximity Point Theorems in Bipolar Metric Spaces with Applications
by Fahad Jahangeer, Salha Alshaikey, Umar Ishtiaq, Tania A. Lazăr, Vasile L. Lazăr and Liliana Guran
Fractal Fract. 2023, 7(10), 766; https://doi.org/10.3390/fractalfract7100766 - 19 Oct 2023
Cited by 2 | Viewed by 1611
Abstract
In this manuscript, we present several types of interpolative proximal contraction mappings including Reich–Rus–Ciric-type interpolative-type contractions and Kannan-type interpolative-type contractions in the setting of bipolar metric spaces. Further, taking into account the aforementioned mappings, we prove best proximity point results. These results are [...] Read more.
In this manuscript, we present several types of interpolative proximal contraction mappings including Reich–Rus–Ciric-type interpolative-type contractions and Kannan-type interpolative-type contractions in the setting of bipolar metric spaces. Further, taking into account the aforementioned mappings, we prove best proximity point results. These results are an extension and generalization of existing ones in the literature. Furthermore, we provide several nontrivial examples, an application to find the solution of an integral equation, and a nonlinear fractional differential equation to show the validity of the main results. Full article
18 pages, 325 KiB  
Article
Almost Ćirić Type Contractions and Their Applications in Complex Valued b-Metric Spaces
by Muhammad Sarwar, Syed Khayyam Shah, Zoran D. Mitrović, Aiman Mukheimer and Nabil Mlaiki
Axioms 2023, 12(8), 794; https://doi.org/10.3390/axioms12080794 - 16 Aug 2023
Cited by 3 | Viewed by 1417
Abstract
In this article, we present the use of a unique and common fixed point for a pair of mappings that satisfy certain rational-type inequalities in complex-valued b-metric spaces. We also provide applications related to authenticity concerns in integral equations. Our results combine well-known [...] Read more.
In this article, we present the use of a unique and common fixed point for a pair of mappings that satisfy certain rational-type inequalities in complex-valued b-metric spaces. We also provide applications related to authenticity concerns in integral equations. Our results combine well-known contractions, such as the Ćirić contraction and almost contractions. Full article
(This article belongs to the Special Issue Fixed Point Theory and Its Related Topics IV)
23 pages, 371 KiB  
Article
Solutions of Fractional Differential Inclusions and Stationary Points of Intuitionistic Fuzzy-Set-Valued Maps
by Monairah Alansari and Mohammed Shehu Shagari
Symmetry 2023, 15(8), 1535; https://doi.org/10.3390/sym15081535 - 3 Aug 2023
Cited by 2 | Viewed by 1110
Abstract
One of the tools for building new fixed-point results is the use of symmetry in the distance functions. The symmetric property of metrics is particularly useful in constructing contractive inequalities for analyzing different models of practical consequences. A lot of important invariant point [...] Read more.
One of the tools for building new fixed-point results is the use of symmetry in the distance functions. The symmetric property of metrics is particularly useful in constructing contractive inequalities for analyzing different models of practical consequences. A lot of important invariant point results of crisp mappings have been improved by using the symmetry of metrics. However, more than a handful of fixed-point theorems in symmetric spaces are yet to be investigated in fuzzy versions. In accordance with the aforementioned orientation, the idea of Presic-type intuitionistic fuzzy stationary point results is introduced in this study within a space endowed with a symmetrical structure. The stability of intuitionistic fuzzy fixed-point problems and the associated new concepts are proposed herein to complement their corresponding concepts related to multi-valued and single-valued mappings. In the instance where the intuitionistic fuzzy-set-valued map is reduced to its crisp counterparts, our results complement and generalize a few well-known fixed-point theorems with symmetric structure, including the main results of Banach, Ciric, Presic, Rhoades, and some others in the comparable literature. A significant number of consequences of our results in the set-up of fuzzy-set- and crisp-set-valued as well as point-to-point-valued mappings are emphasized and discussed. One of our findings is utilized to assess situations from the perspective of an application for the existence of solutions to non-convex fractional differential inclusions involving Caputo fractional derivatives with nonlocal boundary conditions. Some nontrivial examples are constructed to support the assertions and usability of our main ideas. Full article
12 pages, 278 KiB  
Article
Some Results for Ćirić–Prešić Type Contractions in F-Metric Spaces
by Vildan Ozturk
Symmetry 2023, 15(8), 1521; https://doi.org/10.3390/sym15081521 - 1 Aug 2023
Cited by 4 | Viewed by 1129
Abstract
In this study, first, we introduce Ćirić–Prešić type contraction in F-metric spaces and prove a fixed point theorem for self mappings. We apply the fixed point results for a second-order differential equation. Therefore, we define Prešić type almost contraction and F-contraction, [...] Read more.
In this study, first, we introduce Ćirić–Prešić type contraction in F-metric spaces and prove a fixed point theorem for self mappings. We apply the fixed point results for a second-order differential equation. Therefore, we define Prešić type almost contraction and F-contraction, and we prove some fixed point theorems. In the last section, we prove the best proximity point theorems for Ćirić–Prešić type proximal contraction in F-metric spaces. Our results generalize the existing results in the literature. Full article
22 pages, 350 KiB  
Article
Generalized Common Best Proximity Point Results in Fuzzy Metric Spaces with Application
by Umar Ishtiaq, Fahad Jahangeer, Doha A. Kattan and Ioannis K. Argyros
Symmetry 2023, 15(8), 1501; https://doi.org/10.3390/sym15081501 - 28 Jul 2023
Cited by 3 | Viewed by 1683
Abstract
The symmetry of fuzzy metric spaces has benefits for flexibility, ambiguity tolerance, resilience, compatibility, and applicability. They provide a more comprehensive description of similarity and offer a solid framework for working with ambiguous and imprecise data. We give fuzzy versions of some celebrated [...] Read more.
The symmetry of fuzzy metric spaces has benefits for flexibility, ambiguity tolerance, resilience, compatibility, and applicability. They provide a more comprehensive description of similarity and offer a solid framework for working with ambiguous and imprecise data. We give fuzzy versions of some celebrated iterative mappings. Further, we provide different concrete conditions on the real valued functions J,S:(0,1]R for the existence of the best proximity point of generalized fuzzy (J,S)-iterative mappings in the setting of fuzzy metric space. Furthermore, we utilize fuzzy versions of J,S-proximal contraction, J,S-interpolative Reich–Rus–Ciric-type proximal contractions, J,S-Kannan type proximal contraction and J,S-interpolative Hardy Roger’s type proximal contraction to examine the common best proximity points in fuzzy metric space. Also, we establish several non-trivial examples and an application to support our results. Full article
18 pages, 338 KiB  
Article
A Fixed Point Theorem for Generalized Ćirić-Type Contraction in Kaleva–Seikkala’s Type Fuzzy b-Metric Spaces
by Jiaojiao Wu, Fei He and Shufang Li
Axioms 2023, 12(7), 616; https://doi.org/10.3390/axioms12070616 - 21 Jun 2023
Cited by 3 | Viewed by 1386
Abstract
In this paper, we state and establish a new fixed point theorem for generalized Ćirić-type contraction in Kaleva-Seikkala’s type fuzzy b-metric space. Our results improve and extend some well-known results in the literature. Some examples are given to support our result. Finally, [...] Read more.
In this paper, we state and establish a new fixed point theorem for generalized Ćirić-type contraction in Kaleva-Seikkala’s type fuzzy b-metric space. Our results improve and extend some well-known results in the literature. Some examples are given to support our result. Finally, as an application, we show the existence and uniqueness of solution to Volterra integral equation formulated in Kaleva–Seikkala’s type fuzzy b-metric space. Full article
(This article belongs to the Special Issue Differential Equations and Related Topics)
16 pages, 325 KiB  
Article
Some Common Fixed Circle Results on Metric and 𝕊-Metric Spaces with an Application to Activation Functions
by Nihal Taş, Elif Kaplan, Dania Santina, Nabil Mlaiki and Wasfi Shatanawi
Symmetry 2023, 15(5), 971; https://doi.org/10.3390/sym15050971 - 24 Apr 2023
Cited by 5 | Viewed by 1341
Abstract
In this paper, we modify various contractive conditions (C.C.)s such as Ciric type (C.C.), Rhoades type (C.C.), Seghal type (C.C.), Bianchini type (C.C.), and Berinde type (C.C.) for two self-mappings, considering that the contractive property plays a major role in establishing a fixed [...] Read more.
In this paper, we modify various contractive conditions (C.C.)s such as Ciric type (C.C.), Rhoades type (C.C.), Seghal type (C.C.), Bianchini type (C.C.), and Berinde type (C.C.) for two self-mappings, considering that the contractive property plays a major role in establishing a fixed circle (F.C.) on both metric spaces (M-s) and S-(M-s) where the symmetry condition is satisfied, and we utilize them to establish a common (F.C.). We prove new (F.C.) results on both (M-s) and S-(M-s) with illustrative examples. Finally, we provide an application to activation functions such as rectified linear unit activation functions and parametric rectified linear unit activation functions. Full article
(This article belongs to the Special Issue Symmetry Application in Fixed Point Theory)
Show Figures

Figure 1

Back to TopTop