Mappings In Fuzzy Metric Spaces Research Articles

Fixed Point Results for Almost Contraction Mappings in Fuzzy Metric Space

في بعض المسائل الرياضية والحاسوبية والاقتصادية والنمذجة، يكون وجود حل لمشكلة نظرية أو مشكلة في العالم الحقيقي مرادفًا لوجود نقطة صامدة (Fp) لدالة مناسبة. وبالتالي، فأن نظرية النقطة الصامدة Fp تلعب دورًا أساسيًا في مجموعة واسعة من السياقات الرياضية والعلمية. تعتبر نظرية النقطة الصامدة Fp في حد ذاتها مزيجًا مذهلاً مكون من التحليل (التحليل الصرف والتحليل التطبيقي)، والهندسة، والطوبولوجيا. لقد أظهرت السنوات الأخيرة أن نظرية النقطة الصامدة Fp هي أداة قوية ومفيدة للغاية في دراسة الحالات غير الخطية. تهتم نظريات النقطة الصامدة Fp بدالة f من المجموعة X الى المجموعة X نفسها والتي في ظل ظروف معينة، فأنها تسمح بوجود نقطة صامدة Fp ، بعبارة اخرى انه بمعنى لكل نقطة x موجودة في المجموعة X (x∈X) بحيث أن f(x)=x . يقدم هذا العمل ويثبت نظرية النقطة الصامدة Fp لأنواع مختلفة من دوال الانكماش في الفضاء المتري الضبابي (FM-space) والتي تسمى بدالة الانكماش القريبة ودالة الانكماش الضعيفة القريبة ( Ψ̃ ,Φ̃). في البداية، تم التذكير بمفهوم الفضاء المتري الضبابي(FM-space) وبعض المصطلحات المستخدمة في الإطار الضبابي. ثم بعد ذلك تم اعطاء مفهوم دالة المحاكاة. يتم استخدام مفهوم دالة المحاكاة هذا لتقديم تعريف دالة الانكماش Z̃ القريبة في إطار الفضاء المتري الضبابي. بالإضافة إلى ذلك، لقد تم استخدام هذا المفهوم(دالة الانكماش Z̃ القريبة) لبرهان وجود النقطة الصامدة ووحدانية النقطة الصامدة لهذا النوع من الدوال.ثم بعد ذلك تم تقديم فكرة دالة الانكماش الضعيفة القريبة ( Ψ̃ ,Φ̃) في إطار الفضاء المتري الضبابي(FM-space) ، بالإضافة إلى تقديم نظرية النقطة الصامدة Fp لهذا النوع من من الدوال. وفي نهاية البحث تم تقديم بعض الأمثلة لدعم النتائج.

Asymptotic fuzzy contractive mappings in fuzzy metric spaces

Asymptotic fuzzy contractive mappings in fuzzy metric spaces

Coincidence Point of Edelstein Type Mappings in Fuzzy Metric Spaces and Application to the Stability of Dynamic Markets

In this paper, we prove a coincidence point result for a pair of mappings satisfying Edelstein-type contractive condition on fuzzy metric spaces. We describe the equilibrium of a simple demand–supply model of a dynamic market by the coincidence point of demand and supply functions. With the help of the coincidence point theorem in fuzzy metric spaces, it is showed that a dynamic market of a supply-sensitive nature (or demand-sensitive nature) always tends towards its equilibrium.

Fixed-point results for fuzzy generalized β-F-contraction mappings in fuzzy metric spaces and their applications

In this paper, we introduce fuzzy generalized β-F-contractions as a generalization of fuzzy F-contractions with admissible mappings. We deduce sufficient conditions for the existence and uniqueness of fixed points for fuzzy generalized β-F-contractions in complete strong fuzzy metric spaces. Our results generalize several fixed-point results from the literature. We present an application of our main result.

Fixed points which belong to the set of unit values of a suitable function on fuzzy metric spaces

In this paper, we introduce the notion of fuzzy (F, φ,β-ψ)-contractive mappings in fuzzy metric spaces and utilize the same to prove some existence and uniqueness fuzzy φ-fixed point results in both M-complete and G-complete fuzzy metric spaces. The obtained results extend, generalize and improve some relevant results of the existing literature. An illustrative example is utilized to demonstrate the usefulness and effectiveness of our results.

An Extended Result on Sub-compatible and Sub-sequential Continuous Maps in Fuzzy Metric Space

An Extended Result on Sub-compatible and Sub-sequential Continuous Maps in Fuzzy Metric Space

Common fixed-point theorems via notion of Pairwise Semi-Compatible Mappings and Occasionally Weakly Compatible Mappings (OWC) for six self-mappings in fuzzy metric spaces

The notion of occasionally weakly compatible mappings, and Semi compatible mappings in fuzzy metric space is discussed in this research. The paper investigates the Common fixed-point theorems in fuzzy metric spaces. By taking the property of commutativity of pair mappings, the pairwise semi-compatible mappings and occasionally weakly compatible mappings, satisfying constructive type condition for six self-mappings the common fixed-point theorems in fuzzy metric spaces were proved. The result improves and generalizes other similar results in the literature.

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.

Best Proximity Point Theorems for the Generalized Fuzzy Interpolative Proximal Contractions

The idea of best proximity points of the fuzzy mappings in fuzzy metric space was intorduced by Vetro and Salimi. We introduce a new type of proximal contractive condition that ensures the existence of best proximity points of fuzzy mappings in the fuzzy complete metric spaces. We establish certain best proximity point theorems for such proximal contractions. We improve and generalize the fuzzy proximal contractions by introducing Ψ,Φ-fuzzy proximal contractions and Ψ,Φ-fuzzy proximal interpolative contractions. The obtained results improve and generalize many best proximity point theorems published earlier. Moreover, we provide many nontrivial examples to validate our best proximity point theorem.

On Some New Common Fixed Point Results for Finite Number of Mappings in Fuzzy Metric Spaces

We essentially suggest the concept of mutual sequences and Cauchy mutual sequence and utilize the same to prove the existence and uniqueness of common fixed point results for finite number of self- and non-self-mappings using fuzzy ℤ ∗ -contractive mappings in fuzzy metric spaces. Our main result was obtained under generalized contractive condition in the fuzzy metric spaces. We provide examples to vindicate the claims and usefulness of such investigations. In this way, the present results generalize and enrich the several existing literature of the fuzzy metric spaces.

Some results on weakly semi compatible mappings in fuzzy metric space

The purpose of this paper is to generate two fixed point theorems in complete fuzzy metric space by using the concepts of weakly semi compatible mappings, sub sequentially continuous mappings and occasionally weakly compatible mappings. Further these results are validated by discussing suitable examples.

The periodic points of ε-contractive maps in fuzzy metric spaces

<p>In this paper, we introduce the notion of ε-contractive maps in fuzzy metric space (X, M, ∗) and study the periodicities of ε-contractive maps. We show that if (X, M, ∗) is compact and f : X −→ X is ε-contractive, then P(f) = ∩ ∞n=1f n (X) and each connected component of X contains at most one periodic point of f, where P(f) is the set of periodic points of f. Furthermore, we present two examples to illustrate the applicability of the obtained results.</p>

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.

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.

Fixed Point Results for (α-βk,ϕ-ψ) Integral Type Contraction Mappings in Fuzzy Metrics

In this paper, we introduce the notion of a modified \((\alpha\)-\(\beta_k,\phi\)-\(\psi)\) integral type contraction mappings in fuzzy metric spaces. We study and prove the existence and uniqueness of fixed points theorems in generalized fuzzy contractive mappings of integral type in fuzzy metric spaces. Our main result generalizes the fuzzy Banach contraction theorem and we validate our results by some suitable examples which reveal that our results are proper generalization and modification of some researchers' integral contraction works.

Some common fixed point theorems for sequence of self mappings in fuzzy metric space with property (CLRg)

In this research article we generalize and improve the results of K. Jha and V. Pant [K. Jha and V. Pant, Some Common fixed point theorem in fuzzy metric space with property (E.A.), Thai Journal of Mathematics, Vol 15, No.1 (2017), 217-226] using weak compatible maps along with property (CLRg).We also demonstrate an example in support of our main result. K.Jha and V.Pant proved their main result that is Theorem-A by applying the concept of property (E-A),to prove this result they take closeness of range of subspaces that is they proved their main result by using stronger contractive conditions, while in this paper we prove the same result as a Theorem 3.1 by removing the condition of ‘closeness of range of subspaces’ and instead of applying the concept of property (E-A) we do apply the concept of property (CLRg).The importance of property ‘CLR’(Common Limit in Range) ensures that one does not require the closeness of range subspaces. That is we prove the same result for a weaker contractive conditions. By proving the result as Theorem-A, Jha and Pant improved and generalized many similar results on fixed points. The purpose of this paper is to further improve and generalize the result of Jha and Pant and some earlier similar results on fixed point.

Common fixed points using (ψ,ϕ ) - type contractive maps in fuzzy metric spaces

This In this paper, we define new control functions to give unique fixed point in fuzzy metric space. A fruitful contractive condition of (ψ, ϕ)- type is used to obtain common fixed point theorem for two maps in fuzzy metric spaces. We extend the existing results in metric space to fuzzy metric space using these control functions. The first theorem is the extension of the result of Zhang and Song (2009) under the required contractive conditions. Second result is analogous to the result of Doric (2009) in metric spaces.

Some common fixed point theorems for sequence of self mappings in fuzzy metric space with property (CLRg)

In this research article we generalize and improve the results of K. Jha and V. Pant [K. Jha and V. Pant, Some Common fixed point theorem in fuzzy metric space with property (E.A.), Thai Journal of Mathematics, Vol 15, No.1 (2017), 217-226] using weak compatible maps along with property (CLRg).We also demonstrate an example in support of our main result. K.Jha and V.Pant proved their main result that is Theorem-A by applying the concept of property (E-A),to prove this result they take closeness of range of subspaces that is they proved their main result by using stronger contractive conditions, while in this paper we prove the same result as a Theorem 3.1 by removing the condition of ‘closeness of range of subspaces’ and instead of applying the concept of property (E-A) we do apply the concept of property (CLRg).The importance of property ‘CLR’(Common Limit in Range) ensures that one does not require the closeness of range subspaces. That is we prove the same result for a weaker contractive conditions. By proving the result as Theorem-A, Jha and Pant improved and generalized many similar results on fixed points. The purpose of this paper is to further improve and generalize the result of Jha and Pant and some earlier similar results on fixed point.

Fixed point theorems for asymptotically regular mappings in fuzzy metric spaces

The aim of this paper is to extend some existing fixed point results for asymptotically regular mappings to fuzzy metric spaces. For this purpose some contractive type conditions with respect to an altering distance function are used. Some new common fixed point results have been derived for such mappings. We provide suitable examples to justify our study.

Generalization of Singh’s Common Fixed Point Theorem

In this article, I generalize Singh’s common fixed point theorem for compatible mappings in fuzzy metric spaces. Examples are given to support the results proved herein.