Fuzzy Contractive Mappings Research Articles

Note on Intuitionistic Fuzzy Metric-like Spaces with Application in Image Processing

Recently, the fixed-point theorem for fuzzy contractive mappings has been investigated within the framework of intuitionistic fuzzy metric-like spaces. This interesting topic was explored through the utilization of G-Cauchy sequences as defined by Grabiec. The aim of this study is to enhance the aforementioned results in a few aspects. Initially, the proof of the fixed-point theorem is simplified and condensed, allowing for potential generalization to papers focusing on similar fixed-point analyses. Furthermore, instead of G-Cauchy sequences, the classical Cauchy sequences proposed by George and Veeramani are examined, incorporating an additional condition on the fuzzy metric. Within this context, a solution to an old unresolved question posed by Gregory and Sapena is provided. The findings are reinforced by relevant examples. Finally, the introduced fuzzy metrics are applied to the field of image processing.

Asymptotic fuzzy contractive mappings in fuzzy metric spaces

Asymptotic fuzzy contractive mappings in fuzzy metric spaces

Coincidence Point Results for a New Class of Fuzzy Contractive Mappings

This work is mainly aimed to enhance the concept of fuzzy Z-contractive mapping [11] by establish a different contraction called fuzzy (Z,g)- contraction. we obtain some sufficient conditions for the existence and uniqueness of point of coincidence of fuzzy (Z,g)- contraction mappings in the context of fuzzy metric spaces and prove some intriguing results.

RATIONAL TYPE INTUITIONISTIC FUZZY CONTRACTION RESULTS IN INTUITIONISTIC FUZZY METRIC SPACES WITH AN APPLICATION

The purpose of this study is to propose a new idea of rational type intuitionistic fuzzy contraction mappings in intuitionistic fuzzy metric spaces. We show several fixed point results in intuitionistic fuzzy metric spaces under rational type intuitionistic fuzzy contraction conditions, with detailed examples to back up our claims. This revolutionary idea will be crucial in the theory of intuitionistic fuzzy fixed point outcomes and can be applied to other contractive type mappings in the setting of intuitionistic fuzzy metric spaces. Furthermore, to support our work, we offer an application of a nonlinear integral type problem to obtain the current result for a unique solution.

Exploring Fuzzy Triple Controlled Metric Spaces: Applications in Integral Equations

In this article, we delve into the study of fuzzy triple controlled metric spaces, investigating their properties and presenting a range of illustrative examples. We emphasize the broader applicability of this concept in comparison to fuzzy rectangular metric spaces and fuzzy rectangular b-metric spaces. By introducing the novel concept of (α-ψ)-fuzzy contractive mappings, we derive fixed point results specifically designed for complete fuzzy triple controlled metric spaces. Our theorems extend and enrich previous findings in this field. Additionally, we demonstrate the practical significance of our study by applying our findings to the solution of an integral equation and providing an example of its application. Furthermore, we propose potential avenues for future research endeavors.

On α ̌–φ ̆-Fuzzy Contractive Mapping in Fuzzy Normed Space

تمثل فكرة النقاط الصامدة إحدى أقوى الأدوات الرياضية. الغرض الرئيسي من هذه الورقة هو تقديم نوع جديد من دالة الانكماش الضبابي في فضاء معياري ضبابي وهي "الدالة الانكماشية الضبابية ". نثبت بعض نتائج النقطه الصامدة لهذه الداله في سياق الفضاء المعياري الضبابي باستخدام الخاصية المثلثية للمعيار الضبابي. بالإضافة إلى ذلك ، في ظل ظروف محددة ، تم إثبات بعض النتائج الأخرى لهذا النوع من الدالة. أخيرًا ، يتم تقديم مثال لإظهار فائدة النتائج.

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.

Some Fixed Point Theorems in Extended Fuzzy Metric Spaces

In this article, we would like to present a newly fuzzy contraction mapping and using it we would like to prove a fixed point theorem. In fact, we transfer this contraction mapping, first defined in metric spaces [15], and then transferred to fuzzy metric spaces [9] with modification, to extended fuzzy metric spaces [6]. And so we prove some fixed point theorems [9] existing in the literature in the new spaces [6].

Fixed-point theorems in extended fuzzy metric spaces via $\alpha-\phi-\mathcal{M}^{0}$ and $\beta-\psi-\mathcal{M}^{0}$ fuzzy contractive mappings

In this article we would like to present a new type of fuzzy contractive mappings which are called $\alpha-\phi-\mathcal{M}^{0}$ fuzzy contractive and $\beta-\psi-\mathcal{M}^{0}$ fuzzy contractive, and then we demonstrate two theorems which ensure the existence of a fixed point for these two types of mappings. And so we combine and generalize some existing notions in the literature ([5], [7]). Proved these theorems in the extended fuzzy metric spaces are in the more general version than the existing in the literature ones.

Fixed-Point Results for (α-ψ)-Fuzzy Contractive Mappings on Fuzzy Double-Controlled Metric Spaces

We introduce the novel concept of (α-ψ)-fuzzy contractive mappings on fuzzy double-controlled metric spaces and demonstrate some fixed-point results. The theorems presented generalize some intriguing findings in the literature. Thus, we prove the fixed-point theorem in the settings of fuzzy double-controlled metric spaces. Furthermore, we provide several examples and an application of our result on the existence of the solution to an integral equation.

Fixed point results for contractive mappings in fuzzy metric spaces and its applications

In this paper, we introduce a new fuzzy contraction mapping and prove that such mappings have fixed point in τ-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 the existence and uniqueness of the solutions for nonlinear Volterra integral equations on a kind of particular fuzzy metric space.

SOME COMMON FIXED POINT THEOREMS FOR FUZZY TYPE RATIONAL CONTRACTIVE MAPPINGS IN HILBERT SPACES

Heilpern [1] introduced and studied the concept of fuzzy mappings and proved some fixed point theorems for fuzzy contraction mappings. Subsequently several authors studied and generalized the existence of fixed points and common fixed points of fuzzy mappings satisfying various contraction type conditions in metric spaces (see [2],[3],[4],[5], and others). Dutta P.N and Choudhury B.S [6] studied some fixed points for fuzzy mappings in Hilbert spaces. Further Shrivastava R. et al. [7] proved a common fixed point theorem for fuzzy type mapping in Hilbert space. Motivated by the results in [6, 7], we prove three common fixed point theorems for fuzzy rational type mappings in Hilbert spaces. The results extend and generalize many previous known results in the literature.

An Application to Nonlinear Fractional Differential Equation via α-ΓF-Fuzzy Contractive Mappings in a Fuzzy Metric Space

In this paper, we first introduce a new family of functions like an implicit function called Γ-functions. Furthermore, we introduce a new concept of α-ΓF-fuzzy contractive mappings, which is weaker than the class of fuzzy F-contractive mappings. Then, the existence and uniqueness of the fixed point are established for a new type of fuzzy contractive mappings in the setting of fuzzy metric spaces. Moreover, some examples and an application to nonlinear fractional differential equation are given, and these show the importance of the introduced theorems in fuzzy settings.

Intuitionistic Fuzzy Double Controlled Metric Spaces and Related Results

In this article, we introduce the concept of intuitionistic fuzzy double controlled metric spaces that generalizes the concept of intuitionistic fuzzy b-metric spaces. For this purpose, two noncomparable functions are used in triangle inequalities. We generalize the concepts of the Banach contraction principle and fuzzy contractive mappings by giving authentic proof of these mappings in the sense of intuitionistic fuzzy double controlled metric spaces. To validate the superiority of these results, examples are imparted. A possible application to solving integral equations is also set forth towards the end of this work to support the proposed results.

A new contribution in fuzzy cone metric spaces by strong fixed point techniques with supportive application

In this manuscript, the concept of a cyclic tripled type fuzzy cone contraction mapping in the setting of fuzzy cone metric spaces is introduced. Also, some theoretical results concerned with tripled fixed points are given without a mixed monotone property in the mentioned space. Moreover, under this concept, some strong tripled fixed point results are obtained. Ultimately, to support the theoretical results non-trivial examples are listed and the existence of a unique solution to a system of integral equations is presented as an application.

Common fixed points of fuzzy set-valued contractive mappings on metric spaces with a directed graph

<abstract><p>We introduce a new class of generalized graphic fuzzy $ F $- contractive mappings on metric spaces and establish the existence of common fuzzy coincidence and fixed point results for such contractions. It is significant to note that we do not use any form of continuity of mappings to prove these results. Some examples are provided to verify our proven results. Various developments in the existing literature are generalized and extended by our results. It is aimed that the initiated concepts in this work will encourage new research aspects in fixed point theory and related hybrid models in the literature of fuzzy mathematics.</p></abstract>

Some Rational Coupled Fuzzy Cone Contraction Theorems in Fuzzy Cone Metric Spaces with an Application

In this paper, we establish the new concept of rational coupled fuzzy cone contraction mapping in fuzzy cone metric spaces and prove some unique rational-type coupled fixed-point theorems in the framework of fuzzy cone metric spaces by using “the triangular property of fuzzy cone metric.” To ensure the existence of our results, we present some illustrative unique coupled fixed-point examples. Furthermore, we present an application of a Lebesgue integral-type contraction mapping in fuzzy cone metric spaces and to prove a unique coupled fixed-point theorem.

Fixed Point Results for Generalized Fuzzy Contractive Mappings in Fuzzy Metric Spaces with Application in Integral Equations

In this paper, we introduce generalized α - η -fuzzy contractive mappings and generalized β - ζ -fuzzy contractive mappings and prove existence of fixed point for such mappings. Our results generalize and improve the recent work of Gopal and Vetro (Iranian journal of fuzzy systems, 11 (2014), 95–107). Some equivalent conditions of our results are presented. Also, an example is given to support our new results.

Fixed Point Property Of Lebesgue Fuzzy Metric Spaces With Contraction Conditions

In this paper, we using contraction fuctions in complete fuzzy metric space and establish sequential characterization properties of Lebesgue fuzzy metric space. We prove the existence of common fixed point theorems for contractions mapping in fuzzy metric space using the property of Lebesgue fuzzy metric space and give a few models on the side of our outcomes. We also inaugurate some motivating results based on Lebesgue complete fuzzy contractive mappings.

Rational Type Fuzzy-Contraction Results in Fuzzy Metric Spaces with an Application

This paper aims to introduce the new concept of rational type fuzzy-contraction mappings in fuzzy metric spaces. We prove some fixed point results under the rational type fuzzy-contraction conditions in fuzzy metric spaces with illustrative examples to support our results. This new concept will play a very important role in the theory of fuzzy fixed point results and can be generalized for different contractive type mappings in the context of fuzzy metric spaces. Moreover, we present an application of a nonlinear integral type equation to get the existing result for a unique solution to support our work.