Contraction Principle Research Articles

Existence Analysis of Conformable Fractional Boundary Value Problems

This study examined the fractional boundary value issue at flexible derivatives, focusing on establishing the existence of solutions and uniqueness. We introduce conditions that advance our understanding of this complex mathematical domain by capitalizing on the innovative framework of contraction principles. Moreover, the versatility of the proposed method is emphasized by its effectiveness in dealing with a wide set for compatible fractional differential equations characterized by diverse boundary conditions.

Convergence results for controlled contractions and applications to a system of Volterra integral equations

This work presents the concept of controlled dislocated metric spaces, and the Banach contraction principle in these spaces is examined. Next, we provide extensive examples of numerical convergence of fixed points to demonstrate the practical implications of such spaces. Along with specific instances, it presents the idea of a rational contraction of the ϝ − type to determine common fixed points in such spaces. Moreover, numerical analysis and graphical comparisons are used to further assess the existence of common fixed points based on the provided notions. Lastly, using these ideas to solve a Volterra integral equation shows how useful they are for finding common solutions, improving our comprehension of fixed point theory in these spaces, and creating new avenues for applications.

Analysis of Cauchy reaction-diffusion equations involving Atangana-Baleanu fractional operator

This study investigates the Cauchy reaction-diffusion equation (CRDE) with the Atangana-Baleanu differential operator. The existence and uniqueness of solutions to fractional starting value issues are begun using the fixed-point theorem and contraction principle, respectively. The proposed study uses the natural variation iteration technique (NVIM) to get an approximate solution for nonlinear fractional reaction-diffusion equations. This study's approximate answers are compared to other solutions found using known methodologies, and the results are discussed. The devised technique has benefits in terms of accuracy and computational cost efficiency, which may be used to solve nonlinear fractional reaction-diffusion equations.

Ride-Hailing Drivers’ Preference for Fairwork Principles of Trustworthy Labour-Platform Management and Greater Worker-Autonomy and Willingness to Form and Join Worker-Platform Co-Operatives in Kenya

Ride-hailing worker-platform co-operatives had emerged as part of and for at least fairwork principles. Moreover, studies on e-drivers have recommended the formation of worker-platform co-operatives in Kenya. The actual worker-platform co-operatives by e-drivers are yet to be established. It was against this backdrop that a study was conducted to determine the extent of ride-hailing drivers’ preference for fairwork principles of trustworthy labour-platform management, greater worker-autonomy and willingness to form and join worker-platform co-operatives. The study was grounded in the social exchange theory, affective theory of social exchange, and utility theory. The researcher applied critical-realism research philosophy and multimethod research designs of discrete choice experiments and sequential explanatory mixed method research designs. Using the Yamane sampling formula, the study used quantitative data from 497 respondents from sampled 600 of the 20,000 e-drivers in the Nairobi Metropolitan Region. The quantitative data was analysed using multinominal logistic regression. Moreover, the study used qualitative data from 11 participants, analysed using thematic analysis. Results indicated that the two fairwork principles were statistically significant to e-drivers’ willingness to form and join worker-platform co-operatives. The trustworthy platform management (TPM) principle, in particular, was a highly preferred fairwork principle in terms of e-drivers’ willingness to form and join worker-platform co-operative model (Coeff=2.62; SE = 0.400, Z = 6.54, p< .001), compared to the greater worker-autonomy contract (GAC) principle (Coeff=1.565, SE = 0.202, Z = 7.74, p< .001). This study brings practical and theoretical contributions to improve the e-drivers’ benefits from the ride-hailing sector. Policymakers, promoters, and platform workers like e-drivers could understand how best to promote worker-platform co-operatives to succeed in the country’s societal context.

On the Family of Theorems on Metric Completeness

There have appeared a large family of theorems related the metric completeness. They are mainly concerned with generalizations of the Banach contraction on quasi-metric spaces and their extended artificial spaces. In this survey article, we classify the family according to our 2023 Metatheorem. Many known metric fixed point theorems belong to the family including the Rus-Hicks-Rhoades (RHR) theorem. Such results on metric spaces are consequences of our generalized forms of the Banach contraction principle for weak contractions or the RHR maps on quasi-metric spaces. We list a large number of examples of metric fixed point theorems which follow from our principles. Moreover, we add some comments on related papers in order to improve them.

Compliant Grasp Control Method for the Underactuated Prosthetic Hand Based on the Estimation of Grasping Force and Muscle Stiffness with sEMG

Human muscles can generate force and stiffness during contraction. When in contact with objects, human hands can achieve compliant grasping by adjusting the grasping force and the muscle stiffness based on the object’s characteristics. To realize humanoid-compliant grasping, most prosthetic hands obtain the stiffness parameter of the compliant controller according to the environmental stiffness, which may be inconsistent with the amputee’s intention. To address this issue, this paper proposes a compliant grasp control method for an underactuated prosthetic hand that can directly obtain the control signals for compliant grasping from surface electromyography (sEMG) signals. First, an estimation method of the grasping force is established based on the Huxley muscle model. Then, muscle stiffness is estimated based on the muscle contraction principle. Subsequently, a relationship between the muscle stiffness of the human hand and the stiffness parameters of the prosthetic hand controller is established based on fuzzy logic to realize compliant grasp control for the underactuated prosthetic hand. Experimental results indicate that the prosthetic hand can adjust the desired force and stiffness parameters of the impedance controller based on sEMG, achieving a quick and stable grasp as well as a slow and gentle grasp on different objects.

The Hell-or-High-Water Clause in Aircraft Leasing Contract: UNIDROIT Principles and the Indonesian Civil Code

This research analyses the hell-or-high-water clause in aircraft leasing contracts in the context of the principle of freedom of contract. Focusing on the review of the principle of freedom of contract based on UNIDROIT Principles of International Commercial Contract (UPICC) 2016 and Indonesian Civil Code, this research uses normative juridical method with analytical descriptive approach. The findings show that the hell-or-high-water clause has a high binding force, providing legal certainty, especially for the lessor. However, its application must be in line with the principle of freedom of contract regulated in UPICC 2016 and the Civil Code. The application of this clause is suggested to consider three limitations stipulated by the UPICC 2016: first, the principle of freedom of contract that allows businesses to choose partners and transaction terms; second, the exclusion of certain sectors in the public interest by the state; and third, mandatory rules that limit the content of the contract. Therefore, the hell-or-high-water clause should be applied with due regard to the implementation of the principle of freedom of contract as well as national law or the existence of compelling national regulations.

On the relation of Kannan contraction and Banach contraction

Abstract Kannan contraction is broadly investigated topic in Metric Fixed Point Theory due to its importance in omitting the continuity presumption. Of a great significance is also its role in characterizing completeness of a metric space through existence and uniqueness of a fixed point of arbitrary Kannan contraction in the observed setting. The concept of Kannan contraction has been adapted, extended and transferred to various types of spaces including cone metric spaces, quasi metric spaces, b-metric spaces, partial metric spaces, among others. The main aim of this article is to prove that for any Kannan contraction T on a complete metric space (X, d) there exists another metric on the set X in relation to which T is a Banach contraction while the completeness is preserved. In that way, all results on Kannan contraction may be derived as corollaries of the Banach contraction principle. The converse also holds since, by altering the metric, Banach contraction becomes a Kannan contraction. The obtained theoretical results are substantiated with adequate examples.

On Modular b-Metrics

The notions of modular b-metric and modular b-metric space were introduced by Ege and Alaca as natural generalizations of the well-known and featured concepts of modular metric and modular metric space presented and discussed by Chistyakov. In particular, they stated generalized forms of Banach’s contraction principle for this new class of spaces thus initiating the study of the fixed point theory for these structures, where other authors have also made extensive contributions. In this paper we endow the modular b-metrics with a metrizable topology that supplies a firm endorsement of the idea of convergence proposed by Ege and Alaca in their article. Moreover, for a large class of modular b-metric spaces, we formulate this topology in terms of an explicitly defined b-metric, which extends both an important metrization theorem due to Chistyakov as well as the so-called topology of metric convergence. This approach allows us to characterize the completeness for this class of modular b-metric spaces that may be viewed as an offsetting of the celebrated Caristi–Kirk theorem to our context. We also include some examples that endorse our results.

The Study of Fixed Point Theorem over Modular F-metric Spaces

One of the most significant discoveries in the annals of mathematical history is Schauder's fixed-point theorem, which is generally recognized to be among the most important discoveries. The fact that the Brüwer fixed point hypothesis cannot be used in dimensions of space that are infinitely large is one of the most important discoveries in the history of mathematics. The facts that have been supplied make it feasible to claim that the great majority of them are of a topological nature. In 2019, N. Manav and D. Turkoglu introduced a new class of generalized metric space called modular F metric space as a generalization of metric space. It is generally agreed upon that this is one of the most significant discoveries that has been made in the subject of mathematics that has ever been produced. In this article, we study the basic structure of modular F-metric spaces and the concept of an equivalent relationship between modular F metric space and modular F metric bounded space. Moreover, we study the fixed point theorem (New version of Banach Contraction Principle) over modular F metric spaces. This is something that one would be able to predict occurring given the circumstances that are present. These results extend, broaden, and integrate many previously published results.

RESULTS ON IMPULSIVE ψ-CAPUTO FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH BOUNDARY CONDITIONS

In this research article, we investigate the existence and uniqueness of solutions for a type of boundary value problems involving fractional integro-differential equations with the ψ-Caputo fractional derivative. Our method utilizes several classical fixed point theorems, such as the Banach contraction principle and Krasnoselskii's fixed point theorem. We establish our main results through theoretical analysis and present a specific case study to illustrate the practical significance of our findings.

Enhancing Professional Awareness of Informed Consent : Safeguarding the Rights of Patients and Practitioners.

Informed consent is a crucial communication process between doctors and patients for obtaining patients' approval before initiating medical treatment. It is derived from the legal principles of medical contracts and requires doctors to explain the treatment process to patients. Surgeons should be aware of informed consent not only to avoid unnecessary litigation risks but also to provide patients with the right to self-determination. The aim of the study is to help surgeons in Korea understand the legal doctrine on informed consent for practical application. This article reviews the legal doctrine of IC according to 4W1H-why, who, what, when, and how-with judicial cases to communicate effectively with patients in clinical settings. Regardless of seniority or rank, doctors may provide competent patients with information to protect their rights to self-determination. Informed consent should be advanced for patients to consider, discuss with significant others, and determine whether or not to undergo medical treatment. At that stage, patients need to be informed of the necessity, risks, and so on. The most common method of informed consent is an oral explanation utilizing certain forms for documentation. However, the informed consent of patients can be exempted on certain occasions. Optimal informed consent, when implemented, leads to patient-centered care, which significantly improves patient satisfaction and outcomes. Ultimately, it not only protects doctors from litigation risks but also upholds patients' autonomy.

The Closest Point Theorem in CAT p (0) Metric Spaces

In this work, we investigate the closest point theorem in complete CAT p ( 0 ) metric spaces for p ≥ 2 . As an application, an extension of the Banach Contraction Principle for best proximity points is obtained.

On Fuzzy Fractional Volterra-Fredholm Model Under the Uncertainty θ-Operator of the AD Technique: Theorems and Applications

This article investigates the proper existence conditions and uniqueness results for a class of fuzzy fractional Caputo Volterra-Fredholm integro-differential equations (FFCV-FIDE) with initial conditions. The findings are based on Banach's contraction principle and Schaefer's fixed point theorem. Furthermore, the solution to the posed problem is found using the Adomian decomposition technique (ADT). We support the concept with several examples. The relationship between the upper and lower reduced approximation of the fuzzy solutions was demonstrated numerically and graphically using MATLAB.

The ergodicity and uniform large deviations for the 1D stochastic Landau-Lifshitz-Bloch equation

In this article, we consider two aspects asymptotic behaviors for the 1D stochastic Landau-Lifshitz-Bloch equation driven by additive noise including the unique ergodicity and the uniform large deviations. Using a deterministic argument relying on the exponential moment and exponential stability estimates, we first establish the unique ergodicity of invariant measure in H 1. Then, the uniform large deviations is established in C ( [ 0 , T ] ; H 1 ) by the uniform contraction principle.

Super Metric Space and Fixed Point Results

Banach contraction principle is the beginning of the Metric fixed point theory. This principle gives existence and uniqueness of fixed points and methods for obtaining approximate fixed points. It is the basic tool of finding fixed points of all contraction type maps. It has a constructive proof which makes the theorem worthy because it yields an algorithm for computing a fixed point. Banach fixed point result has been extended by various authors in many directions either by weakening the conditions of contraction mapping or by changing the abstract structure. Several generalizations and extensions of metric spaces have been introduced. Among these, the prominent extensions are b-metric space, fuzzy metric space, partial metric space and a lot more of their combinations. In particular, a new structure namely Super metric space is introduced. In the present paper, we generalize and extend the fixed point results of fixed point theory in literature in the framework of super metric space.

Existence and Ulam stability of initial value problem for fractional perturbed functional q-difference equations

Abstract. In this work, we discuss the existence and uniqueness of solutions to the initial value problem for perturbed functional fractional q-difference equations involving q-derivative of the Caputo sense. By applying Banach contraction principle and Burton and Kirk’s fixed point theorems. Further, we present the Ulam-Hyers and Ulam-Hyers-Rassias stabilities results by using direct analysis methods. Finally, we give two examples illustrating of the results. Mathematics Subject Classification (2010): 26A33, 34A12, 39A13, 47H10. Keywords: Initial value problem, Caputo fractional q-derivative, Burton and Kirk’s fixed point theorem, Ulam-Hyers stability, Ulam-Hyers-Rassias stability.

On Banach Contraction Principle for Generalized Fuzzy Variational Inequality Problems

The main objective of the paper is to study the existence theorem of the newly defined generalized fuzzy ψ-variational inequality problem, generalized fuzzy ψ-complementarity problem. Uniqueness of the problems are also studied. Existence of these problems are established with the help of unique point condition of η. The existence of the solution of generalized fuzzy ψ-variational inequality problems is studied with the help of Banach contraction principle. The existence of the solution of generalized fuzzy ψ-complementarity problem is established in η-invex space.Conclusion: Equality of the solution sets of generalized fuzzy ψ-variational inequality problem and generalized fuzzy ψ-complementarity problem is shown using unique point condition of the bifunction η. Unique of the solution of generalized fuzzy ψ-variational inequality problem and generalized fuzzy ψ-complementarity problem is studied using strictly monotonicity condition. Existence theorems of the solution of generalized fuzzy ψ-variational inequality problem are shown using Banach contraction principle in the presence of Lipschitz continuous, strongly monotone mappings T_ψ and weakly monotonicity of η. Existence theorems of the solution of generalized fuzzy ψ-complementarity problem in the presence of condition C_0.

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The primary objective of this manuscript is to investigate the existence and uniqueness of solutions for the Langevin (k,φ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$(\\mathtt{k},\\varphi )$\\end{document}-Hilfer fractional differential equation of different orders with multipoint nonlocal fractional integral boundary conditions. We consider the generalized version of the Hilfer fractional diferential equation called as (k,φ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$(\\mathtt{k},\\varphi )$\\end{document}-Hilfer fractional differential equation. We provide some significant outcomes about (k,φ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$(\\mathtt{k},\\varphi )$\\end{document}-Hilfer fractional Langevin differential equation that requires deriving equivalent fractional integral equation to (k,φ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$(\\mathtt{k},\\varphi )$\\end{document}-Hilfer Langevin fractional differential equation. The existence result is established using the Krasnoselskii’s fixed-point theorem, while the uniqueness is addressed with the help of Banach contraction principle. Additionally, we investigate the different forms of Ulam stability for the solution of the mentioned problem, under specific conditions. To validate our main outcomes, we present a detailed example at the end of the manuscript.

Some Fixed Point Theorems in Convex S-Metric Space

In this paper, we introduce convex S-metric space. We also establish and prove some fixed point theorems for self-mappings satisfying certain contraction principles on a complete convex S-metric space. Some examples are presented to validate the originality and applicability of our results. Finally, we improve, generalize and extend some recent results.