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

2016 ◽  
Vol 21 (6) ◽  
pp. 811-835 ◽  
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.

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

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1594
Author(s):  
Antonio Francisco Roldán López de Hierro ◽  
Andreea Fulga ◽  
Erdal Karapınar ◽  
Naseer Shahzad
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Complete Metric Spaces ◽  
Auxiliary Functions ◽  
Fuzzy Metric ◽  
New Class

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.

scholarly journals On Fuzzy Contractive Mappings in Fuzzy Metric Spaces

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.

scholarly journals Existence of Solutions for Nonlinear Impulsive Fractional Differential Equations via Common Fixed-Point Techniques in Complex Valued Fuzzy Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Humaira ◽  
Muhammad Sarwar ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Common Fixed Point ◽  
Fractional Differential Equations ◽  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential ◽  
Complex Valued

The main purpose of this paper is to study the existence theorem for a common solution to a class of nonlinear three-point implicit boundary value problems of impulsive fractional differential equations. In this respect, we study the fuzzy version of some essential common fixed-point results from metric spaces in the newly introduced notion of complex valued fuzzy metric spaces. Also, we provide an illustrative example to demonstrate the validity of our derived results.

scholarly journals On Some Fixed Point Results in E − Fuzzy Metric Spaces

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.

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

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.

scholarly journals Fixed Point Results via Least Upper Bound Property and Its Applications to Fuzzy Caputo Fractional Volterra-Fredholm Integro-Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1969
Author(s):  
Humaira ◽  
Muhammad Sarwar ◽  
Thabet Abdeljawad ◽  
Nabil Mlaiki
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Upper Bound ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Multivalued Mappings ◽  
Contractive Condition ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric

In recent years, complex-valued fuzzy metric spaces (in short CVFMS) were introduced by Shukla et al. (Fixed Point Theory 32 (2018)). This setting is a valuable extension of fuzzy metric spaces with the complex grade of membership function. They also established fixed-point results under contractive condition in the aforementioned spaces and generalized some essential existence results in fixed-point theory. The purpose of this manuscript is to derive some fixed-point results for multivalued mappings enjoying the least upper bound property in CVFMS. Furthermore, we studied the existence theorem for a unique solution to the Fuzzy fractional Volterra–Fredholm integro-differential equations (FCFVFIDEs) as an application to our derived result involving the Caputo derivative.

scholarly journals Some φ-Fixed Point Results for (F,φ,α-ψ)-Contractive Type Mappings with Applications

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 122 ◽  
Author(s):  
Mohammad Imdad ◽  
Abdur Khan ◽  
Hayel Saleh ◽  
Waleed Alfaqih
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Existence Result ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Nonlinear Differential Equations ◽  
Partial Metric ◽  
Partial Metric Spaces ◽  
Contractive Type

In this paper, we introduce the notions of (F, φ , α - ψ )-contractions and (F, φ , α - ψ )-weak contractions in metric spaces and utilize the same to prove some existence and uniqueness φ -fixed point results. Some illustrative examples are given to demonstrate the usefulness and effectiveness of our results. As applications, we deduce some fixed point theorems in partial metric spaces besides proving an existence result on the solution of nonlinear differential equations. Our results extend, generalize and improve some relevant results of the existing literature.

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

Mathematics ◽  
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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