Fuzzy Fixed Point Theorems Research Articles

Some Common Fuzzy Fixed Point Theorems on G - Metric Space

The motive of this paper is to give a few not unusual place constant factor theorems in G-Metric spaces, with the aid of using the perception of Common restrict with inside the variety belongings and to illustrate appropriate examples. These outcomes make bigger and generalizes numerous widely known outcomes with inside the literature.

Fuzzy Fixed Point Theorems in Normal Cone Metric Space

In this paper, we proved a few fuzzy fixed point theorems in whole regular cone metric spaces, which can be the generalization of a few current consequences within side the literature.

Suzuki-type fuzzy contractive inequalities in 1-Z-complete fuzzy metric-like spaces with an application

In the piece of this note, we mention various Suzuki-type fuzzy contractive inequalities in 1-Z-complete fuzzy metric-like spaces for uniqueness and existence of a fixed point and prove a few fuzzy fixed point theorems, which are appropriate generalizations of some of the latest famed results in the literature. Mainly, we generalize fuzzy Θ-contraction in terms of Suzuki-type fuzzy Θ-contraction and also fuzzy ϓ-contractive mapping in view of Suzuki-type. For this new group of Suzuki-type functions, acceptable conditions are formulated to ensure the existence of a unique fixed point. The attractive beauty of this fuzzy distance space lies in the symmetry of its variables, which play a crucial role in the construction of our contractive conditions to ensure the solution. Furthermore, a lot of considerable examples are presented to illustrate the significance of our results. In the end, we have discussed an application in an extensive way for the solution of a nonlinear fractional differential equation via Suzuki-type fuzzy contractive mapping.

Chatterjea type theorems for complex valued extended $ b $-metric spaces with applications

<abstract><p>In this article, we establish common $ \alpha $ -fuzzy fixed point theorems for Chatterjea type contractions involving rational expression in complex valued extended $ b $-metric space. Our results generalize and extend some familiar results in the literature. Some common fixed point results for multivalued and single valued mappings are derived for complex valued extended $ b $-metric space, complex valued $ b $-metric space and complex valued metric space as consequences of our leading results. As an application, we investigate the solution of Fredholm integral inclusion.</p></abstract>

Fixed point results of fuzzy mappings with applications

<abstract><p>Jleli and Samet introduced the notion of $ \mathcal{F} $-metric space as a generalization of traditional metric space and proved Banach contraction principle in the setting of these generalized metric spaces. The aim of this article is to utilize $ \mathcal{F} $-metric space and establish some common $ \alpha $-fuzzy fixed point theorems for rational ($ \beta $-$ \phi) $-contractive conditions. Our results extend, generalize and unify some well-known results in the literature. As application of our main result, we discuss the solution of fuzzy integrodifferential equations in the setting of a generalized Hukuhara derivative.</p></abstract>

On interpolative fuzzy contractions with applications

In this paper, following a new interpolation approach in fixed point theory, we introduce the concepts of interpolative Hardy-Rogers-type fuzzy contraction and interpolative Reich-Rus-Ciric type fuzzy contraction in the framework of metric spaces, and we analyze the existence of fuzzy fixed points for such contractions equipped with some suitable hypotheses. A few consequences in single-valued mappings which include the conclusion of the main result of Karapinar et al. [On interpolative Hardy-Rogers type contractions. Symmetry, 2019, 11(1), 8] are obtained. On the basis that fixed point of a single-valued mapping satisfying interpolative type contractive inequality is not necessarily unique, and thereby making the notions more appropriate for fixed point theorems of multifunctions, new multivalued analogues of the fuzzy fixed point theorems presented herein are deduced as corollaries. In addition, nontrivial examples which dwell upon the generality of our results are provided. Finally, one of our results is applied to investigate solvability conditions of a Fredholm integral inclusion.

Fixed point results via hesitant fuzzy mapping on extended b-metric spaces

In the present research article, the notion of hesitant fuzzy mapping, contraction hesitant fuzzy mapping, generalized contraction of hesitant fuzzy mapping are introduced in setting of extended b-metric structure, which in particular case reduced to b-metric space. The newly introduced concepts are used to prove hesitant fuzzy fixed point theorems. The main results have extended and unified recent results in literature. The results are validated with the help of examples. Finally, as an application, the results are applied to solve integral equation of fredholm type.

A fuzzy fixed-point theorem and its applications to maximal elements and Nash equilibria in noncompact CAT(0) spaces

In this paper, based on the KKM method, we prove a new fuzzy fixed-point theorem in noncompact CAT(0) spaces. As applications of this fixed-point theorem, we obtain some existence theorems of fuzzy maximal element points. Finally, we utilize these fuzzy maximal element theorems to establish some new existence theorems of Nash equilibrium points for generalized fuzzy noncooperative games and fuzzy noncooperative qualitative games in noncompact CAT(0) spaces. The results obtained in this paper generalize and extend many known results in the existing literature.

Existence of α L -Fuzzy Fixed Points of L-Fuzzy Mappings

In this research article, fixed point theory is beautifully combined with fuzzy set theory. Two fuzzy fixed point theorems of L-fuzzy mappings are established and proved for two different contractive type conditions in the scenario of complete b-metric space. In order to give the strength of these results, nontrivial supportive examples for both results are also provided. The notion of L-fuzzy mappings is a generalized form of fuzzy mappings as well as multivalued mappings. In this approach, our results provide uniqueness, extension, and successive generalizations of many valuable recent and conventional results existing in the literature.

Fuzzy fixed point theorems and Ulam-Hyers stability of fuzzy set-valued maps

Abstract In this paper, new common fuzzy fixed point theorems for sequence of fuzzy set-valued maps in the framework of complete b-metric spaces are established. Consequently, corresponding fixed point theorems in the setting of point-to-set-valued and single-valued mappings are deduced. A few nontrivial examples which dwell upon the generality of our results are provided. Moreover, following the fact that most available Ulam-Hyers type stability results deal with crisp mappings, we initiate the study of stability and well-posedness of functional inclusions involving fuzzy set-valued maps. It is well-known that solution of any functional inclusion is a subset of an appropriate ambient space. With this information, fuzzy fixed point problem for which the right-hand-side is a cut set of a fuzzy set-valued map is introduced. Furthermore, sufficient conditions for existence of solutions of Cantilever Beam Problem and integral inclusions are investigated to indicate the usability of our obtained results.

Common α -Fuzzy Fixed Point Results with Applications to Volterra Integral Inclusions

The purpose of this paper is to establish some common α -fuzzy fixed point theorems for a pair fuzzy mappings and obtain some results of literature for multivalued mappings. For it, we define the notion of generalized Θ -contractions in the context of b -metric spaces. As applications, we investigate the solutions of Volterra integral inclusions by our established results.

New Generalized Ekeland’s Variational Principle, Critical Point Theorems and Common Fuzzy Fixed Point Theorems Induced by Lin-Du’s Abstract Maximal Element Principle

In this paper, by applying the abstract maximal element principle of Lin and Du, we present some new existence theorems related with critical point theorem, maximal element theorem, generalized Ekeland’s variational principle and common (fuzzy) fixed point theorem for essential distances.

Fuzzy Fixed Point Results in F-Metric Spaces with Applications

In this paper, some concepts of F-metric spaces are used to study a few fuzzy fixed point theorems. Consequently, corresponding fixed point theorems of multivalued and single-valued mappings are discussed. Moreover, one of our obtained results is applied to establish some conditions for existence of solutions of fuzzy Cauchy problems. It is hoped that the established ideas in this work will awake new research directions in fuzzy fixed point theory and related hybrid models in the framework of F-metric spaces.

On nonlinear F-contractive fuzzy mappings

The aim of this paper is to obtain some (common) fuzzy fixed point theorems for fuzzy mappings concerning F- contractions (the concept was introduced in [Wardowski, Fixed Point Theory and Applications, 94 (2012), 1-6]) and Feng - Liu type condition [Feng and Liu, Journal of Mathematical Analysis an d Applications, 317 (2006) 103-112] in compelete metric spaces with/without using the Pompeiu - Hausdorff distance between α-level sets of fuzzy mappings. Our results generalize and strengthen various known results in the literature. An example and an application for the solution of a system of functional equations arising in dynamic programming are given to illustrate the usability of the obtained results.

On a topological fuzzy fixed point theorem and its application to non-ejective fuzzy fractals II

This paper deals mainly with new very general fuzzy fixed point theorems in metric spaces and their application to fuzzy fractals. It is a natural continuation of our paper (2018) [1] which significantly generalizes and improves the results by Diamond, Kloeden and Pokrovskii (1997) [2], where no application was given. Moreover, besides the existence, some further important properties of fixed point sets (in particular, fractals) like their weak local stability, called none-ejectivity in the sense of Browder (1965) [3], will be established.

Fuzzy Fixed Point Theorem for Some Types of Fuzzy Jungck Contractive Mappings In Hilbert Space

In this paper, developed Jungck contractive mappings into fuzzy Jungck contractive and proved fuzzy fixed point for some types of generalize fuzzy Jungck contractive mappings.

On a topological fuzzy fixed point theorem and its application to non-ejective fuzzy fractals

A topological fuzzy fixed point theorem is given, when generalizing and improving the main result by Diamond, Kloeden and Pokrovskii (1997) [1]. Apart from the sole existence, a weak local stability property, called non-ejectivity in the sense of Browder, of fuzzy fixed points is established. This theorem is then applied for obtaining non-ejective fuzzy fractals. An alternative approach via the Knaster–Tarski theorem is also presented.

Fuzzy Fixed Point Theorems for Fuzzy Mappings Viafuzzy ?-Admissible

Fuzzy Fixed Point Theorems for Fuzzy Mappings Viafuzzy ?-Admissible

Some new fuzzy fixed point theorems via distance functions with applications

Some new fuzzy fixed point theorems via distance functions with applications

Fuzzy Fixed Point Theorem for Multivalued \(F\)-Contraction in \(b\)-Metric Spaces

In this work, we introduce and suggest the new concept of multivalued fuzzy \(F\)-contraction mappings in \(b\)-metric spaces. We also establish and prove the existence of an \(\alpha\)-fuzzy fixed point theorem in $b$-metric spaces.