Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces

Very recently, Proinov introduced a great family of contractions in the setting of complete metric spaces that has attracted the attention of many researchers because of the very weak conditions that are assumed on the involved functions. Inspired by Proinov’s results, in this paper, we introduce a new class of contractions in the setting of fuzzy metric spaces (in the sense of George and Veeramani) that are able to translate to this framework the best advantages of the abovementioned auxiliary functions. Accordingly, we present some results about the existence and uniqueness of fixed points for this class of fuzzy contractions in the setting of non-Archimedean fuzzy metric spaces.

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A New Approach to Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces

Mathematics ◽

10.3390/math9233001 ◽

2021 ◽

Vol 9 (23) ◽

pp. 3001

Author(s):

Mi Zhou ◽

Naeem Saleem ◽

Xiaolan Liu ◽

Andreea Fulga ◽

Antonio Francisco Roldán López de Hierro

Keyword(s):

Fixed Point ◽

Fixed Points ◽

Existence And Uniqueness ◽

Metric Spaces ◽

Complete Metric Space ◽

Open Problems ◽

Fuzzy Metric Spaces ◽

Auxiliary Functions ◽

Fuzzy Metric ◽

Contractivity Condition

Very recently, by considering a self-mapping T on a complete metric space satisfying a general contractivity condition of the form ψ(d(Tx,Ty))≤φ(d(x,y)), Proinov proved some fixed-point theorems, which extended and unified many existing results in the literature. Accordingly, inspired by Proinov-type contraction conditions, Roldán López de Hierro et al. introduced a novel family of contractions in fuzzy metric spaces (in the sense of George and Veeramani), whose main advantage is the very weak constraints imposed on the auxiliary functions that appear in the contractivity condition. They also proved the existence and uniqueness of fixed points for the discussed family of fuzzy contractions in the setting of non-Archimedean fuzzy metric spaces. In this paper, we introduce a new family of fuzzy contractions based on Proinov-type contractions for which the involved auxiliary functions are not supposed to satisfy any monotonicity assumptions; further, we establish some new results about the existence and uniqueness of fixed points. Furthermore, we show how the main results in the above-mentioned paper can be deduced from our main statements. In this way, our conclusions provide a positive partial solution to one of the open problems posed by such authors for deleting or weakening the hypothesis of the nondecreasingness character of the auxiliary functions.

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w-Distances on Fuzzy Metric Spaces and Fixed Points

Mathematics ◽

10.3390/math8111909 ◽

2020 ◽

Vol 8 (11) ◽

pp. 1909

Author(s):

Salvador Romaguera

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Fixed Points ◽

Point Theorem ◽

Metric Spaces ◽

Fuzzy Metric Spaces ◽

Complete Metric Spaces ◽

Fuzzy Metric

We propose a notion of w-distance for fuzzy metric spaces, in the sense of Kramosil and Michalek, which allows us to obtain a characterization of complete fuzzy metric spaces via a suitable fixed point theorem that is proved here. Our main result provides a fuzzy counterpart of a renowned characterization of complete metric spaces due to Suzuki and Takahashi.

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FUZZY-PREŠIC-CIRIC OPERATORS AND APPLICATIONS TO CERTAIN NONLINEAR DIFFERENTIAL EQUATIONS

Mathematical Modelling and Analysis ◽

10.3846/13926292.2016.1247303 ◽

2016 ◽

Vol 21 (6) ◽

pp. 811-835 ◽

Cited By ~ 1

Author(s):

Satish Shukla ◽

Dhananjay Gopal ◽

Rosana Rodrıguez-Lopez

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Existence And Uniqueness ◽

Metric Spaces ◽

Nonlinear Differential Equations ◽

Fuzzy Metric Spaces ◽

Fuzzy Metric ◽

New Class

In this paper, we introduce a new class of operators called fuzzy-Preši´cCiri´c operators. For this type of operators, the existence and uniqueness of fixed point ´ in M-complete fuzzy metric spaces endowed with H-type t-norms are established. The results proved here generalize and extend some comparable results in the existing literature. An example is included which illustrates the main result of this paper. Moreover, some applications of our main theorem to the study of certain types of nonlinear differential equations are provided.

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On Fuzzy Contractive Mappings in Fuzzy Metric Spaces

10.21203/rs.3.rs-415770/v1 ◽

2021 ◽

Author(s):

Mohammad Hussein Mohammad Rashid

Keyword(s):

Fixed Point ◽

Metric Space ◽

Existence And Uniqueness ◽

Contraction Mapping ◽

Metric Spaces ◽

Random Operator ◽

Random Solution ◽

Fuzzy Metric Spaces ◽

Fuzzy Metric ◽

Contractive Mappings

Abstract In this paper we introduce a new fuzzy contraction mapping and prove that such mappings have fixed point in $\tau$-complete fuzzy metric spaces. As an application, we shall utilize the results obtained to show the existence and uniqueness of random solution for the following random linear random operator equation. Moreover, we shall show that the existence and uniqueness of the solutions for nonlinear Volterra integral equations on a kind of particular fuzzy metric space.

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Existence and Uniqueness of Fixed Point in Fuzzy Metric Spaces and its Applications

Advances in Intelligent Systems and Computing - Proceedings of the Second International Conference on Soft Computing for Problem Solving (SocProS 2012), December 28-30, 2012 ◽

10.1007/978-81-322-1602-5_24 ◽

2014 ◽

pp. 217-223 ◽

Cited By ~ 3

Author(s):

Vishal Gupta ◽

Naveen Mani

Keyword(s):

Fixed Point ◽

Existence And Uniqueness ◽

Metric Spaces ◽

Fuzzy Metric Spaces ◽

Fuzzy Metric

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On Some Fixed Point Results in E − Fuzzy Metric Spaces

Journal of Mathematics ◽

10.1155/2021/9196642 ◽

2021 ◽

Vol 2021 ◽

pp. 1-6

Author(s):

Rachid Mecheraoui ◽

Zoran D. Mitrović ◽

Vahid Parvaneh ◽

Hassen Aydi ◽

Naeem Saleem

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Additional Condition ◽

Metric Spaces ◽

Fuzzy Metric Spaces ◽

Fuzzy Metric ◽

New Class ◽

Contraction Theorem ◽

Banach Contraction ◽

Banach Contraction Theorem

In the existing literature, Banach contraction theorem as well as Meir-Keeler fixed point theorem were extended to fuzzy metric spaces. However, the existing extensions require strong additional assumptions. The purpose of this paper is to determine a class of fuzzy metric spaces in which both theorems remain true without the need of any additional condition. We demonstrate the wide validity of the new class.

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Proving Fixed Point Theorems Employing Fuzzy $(\sigma,\mathcal{Z})$-Contractive Type Mappings

10.20944/preprints202108.0577.v1 ◽

2021 ◽

Author(s):

Hayel N. Saleh ◽

Mohammad Imdad ◽

Salvatore Sessa ◽

Ferdinando Di Martino

Keyword(s):

Fixed Point ◽

Fuzzy Sets ◽

Existence And Uniqueness ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Contractive Mapping ◽

Uniqueness Theorems ◽

Fuzzy Metric Spaces ◽

Fuzzy Metric ◽

Contractive Type

In this article, the concept of fuzzy $(\sigma,\mathcal{Z})$-contractive mapping has been introduced in fuzzy metric spaces which is an improvement over the corresponding concept recently introduced by Shukla et al. [Fuzzy Sets and system. 350 (2018) 85--94]. Thereafter, we utilized our newly introduced concept to prove some existence and uniqueness theorems in $\mathcal{M}$-complete fuzzy metric spaces. Our results extend and generalize the corresponding results of Shukla et al.. Moreover, an example is adopted to exhibit the utility of newly obtained results.

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Fixed point results on θ-metric spaces via simulation functions

Filomat ◽

10.2298/fil1711365c ◽

2017 ◽

Vol 31 (11) ◽

pp. 3365-3375 ◽

Cited By ~ 4

Author(s):

Ankush Chanda ◽

Bosko Damjanovic ◽

Lakshmi Dey

Keyword(s):

Fixed Point ◽

Fixed Points ◽

Existence And Uniqueness ◽

On Convergence of Fixed Points in Fuzzy Metric Spaces

Abstract and Applied Analysis ◽

10.1155/2013/135202 ◽

2013 ◽

Vol 2013 ◽

pp. 1-6 ◽

Cited By ~ 2

Author(s):

Yonghong Shen ◽

Dong Qiu ◽

Wei Chen

Keyword(s):

Fixed Point ◽

Fixed Points ◽

Metric Spaces ◽

Fixed Point Theory ◽

Research Direction ◽

Point Theory ◽

Fuzzy Metric Spaces ◽

Contraction Mappings ◽

Fuzzy Metric

We mainly focus on the convergence of the sequence of fixed points for some different sequences of contraction mappings or fuzzy metrics in fuzzy metric spaces. Our results provide a novel research direction for fixed point theory in fuzzy metric spaces as well as a substantial extension of several important results from classical metric spaces.

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The Study of Fixed Point Theory for Various Multivalued Non-Self-Maps

Abstract and Applied Analysis ◽

10.1155/2013/938724 ◽

2013 ◽

Vol 2013 ◽

pp. 1-9 ◽

Cited By ~ 5

Author(s):

Wei-Shih Du ◽

Erdal Karapınar ◽

Naseer Shahzad

Keyword(s):

Fixed Point ◽

Fixed Points ◽

Existence And Uniqueness ◽

Metric Spaces ◽

Coincidence Point ◽

Fixed Point Theory ◽

Point Theory ◽

Coincidence Points ◽

Complete Metric Spaces

The basic motivation of this paper is to extend, generalize, and improve several fundamental results on the existence (and uniqueness) of coincidence points and fixed points for well-known maps in the literature such as Kannan type, Chatterjea type, Mizoguchi-Takahashi type, Berinde-Berinde type, Du type, and other types from the class of self-maps to the class of non-self-maps in the framework of the metric fixed point theory. We establish some fixed/coincidence point theorems for multivalued non-self-maps in the context of complete metric spaces.

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