Contraction Principle Research Articles

Wardowski Contraction on Controlled S-Metric Type Spaces with Fixed Point Results

This article presents the concept of a triple controlled S-metric type space, characterized by three control functions: β, µ, and γ. This extends the idea of controlled S-metric type spaces. We explore several properties and provide illustrative examples. Furthermore, we introduce αs-admissible mappings and enhance Wardowski’s contraction principle by introducing (αs-F)-contractive mappings specifically designed for triple controlled S-metric type spaces. The article establishes the existence and uniqueness of fixed points within a complete triple controlled S-metric type space. Finally, we apply our main theorem to demonstrate the determination of a unique solution for an mth degree polynomial.

New attitude on sequential Ψ-Caputo differential equations via concept of measures of noncompactness

In this paper, we have explored the existence and uniqueness of solutions for a pair of nonlinear fractional integro-differential equations comprising of the Ψ-Caputo fractional derivative and the Ψ-Riemann–Liouville fractional integral. These equations are subject to nonlocal boundary conditions and a variable coefficient. Our findings are drawn upon the Mittage–Leffler function, Babenko’s attitude, and topological degree theory for condensing maps and the Banach contraction principle. To further elucidate our principal outcomes, we have presented two illustrative examples.

Kedudukan Peranan Notaris dalam Akad Murabahah di Bank Syariah

Basically, the existence of guarantees in sharia banking is a form of bank confidence in the ability of prospective customers who receive facilities to pay off and return the facilities they receive. The aim of this research is: To analyze legal certainty in the financing philosophy of Murabahah contracts in Sharia Banking. And to analyze the role of notaries in murabahah contracts in Sharia banks. Types of legal research are divided into 2 (two) types, namely Normative Legal research and Empirical Legal research. The type of research used by researchers in this research is researchBased on the results of the discussion, the position of Murabahah financing in Sharia Banks is the most popular among the public. Murabahah financing is a product that does not recognize usury or the interest system and murabahah products really help people to make their wishes come true. And the function of a notary is very important in the field of sharia banking, especially in making contracts to channel funds through financing to customers, specifically to create legal certainty in the legal relationship between sharia banks or sharia business units and their customers, namely by making contracts. The financing is in the form of an authentic deed based on the principles of freedom of contract and sharia principles.

Explicit and approximate solutions for a classical hyperbolic fragmentation equation using a hybrid projected differential transform method

Population balance equations are widely used to study the evolution of aerosols, colloids, liquid–liquid dispersion, raindrop fragmentation, and pharmaceutical granulation. However, these equations are difficult to solve due to the complexity of the kernel structures and initial conditions. The hyperbolic fragmentation equation, in particular, is further complicated by the inclusion of double integrals. These challenges hinder the analytical solutions of number density functions for basic kernel classes with exponential initial distributions. To address these issues, this study introduces a new approach combining the projected differential transform method with Laplace transform and Padé approximants to solve the hyperbolic fragmentation equation. This method aims to provide accurate and efficient explicit solutions to this challenging problem. The approach's applicability is demonstrated through rigorous mathematical derivation and convergence analysis using the Banach contraction principle. Additionally, several numerical examples illustrate the accuracy and robustness of this new method. For the first time, new analytical solutions for number density functions are presented for various fragmentation kernels with gamma and other initial distributions. This method significantly enhances solution quality over extended periods using fewer terms in the truncated series. The solutions are compared and verified against the finite volume method and the homotopy perturbation method, showing that the coupled approach not only estimates number density functions accurately but also captures integral moments with high precision. This research advances computational methods for particle breakage phenomena, offering potential applications in various industrial processes and scientific disciplines.

Stability Analysis Study of Time-Fractional Nonlinear Modified Kawahara Equation Based on the Homotopy Perturbation Sadik Transform

In this manuscript, we survey a numerical algorithm based on the combination of the homotopy perturbation method and the Sadik transform for solving the time-fractional nonlinear modified shallow water waves (called Kawahara equation) within the frame of the Caputo–Prabhakar (CP) operator. The nonlinear terms are handled with the assistance of the homotopy polynomials. The stability analysis of the implemented method is studied by using S-stable mapping and the Banach contraction principle. Also, we use the fixed-point method to determine the existence and uniqueness of solutions in the given suggested model. Finally, some numerical simulations are illustrated to display the accuracy and efficiency of the present numerical method. Moreover, numerical behaviors are captured to validate the reliability and efficiency of the scheme.

National And Public Interest Perspective on the Governance and Regulation of Carbon Capture and Storage Implementation in Indonesia

Recently Indonesian Government issued two important regulations regarding Carbon Capture Storage (CCS) namely, President Regulation No. 14/2024 and Ministry of Energy and Mineral Resources Regulations No. 2/2003. Both regulations have caused Indonesia's CCS Legal and Regulatory score by the Global CCS Institute to increase significantly. There are three criteria applied by the Global CCS Institute to define the score: regulation of trans boundaries movement of CCS, specific legal and regulatory framework, and facilitation of early project. Despite the increase in CCS score, some essential questions remain as crucial problems that are not solvable easily. Those questions regarding the national and common interest of Indonesian people by the issuance of both legal and regulations are still unclear, at least from the common people's perspective. The Presidential Regulation define dual schemes for CCS implementation: Contract Scheme and Permit Scheme. From the common people's perspective, both schemes need to be exercised further to respond to the public questions properly. Therefore, any reason behind the implementation of those two schemes as well as any potential benefit for Indonesia by implementing those two schemes in parallel are very important to be reviewed and analyzed. Reinforcement of Oil and Gas Production Sharing Contract Principles in the implementation of CCS in Indonesia are more favourable for the National and Public Interest Perspective.

System of Nonlinear (<i>k</i>, ψ)-Hilfer Fractional Order Hybrid Boundary Value Problems

This paper focuses on the existence and uniqueness of solutions for a new class of coupled fractional differential equations subject to specific boundary conditions. We introduce a novel approach that incorporates the (k, ψ)-Hilfer fractional derivative, a recent advancement in fractional calculus. By leveraging the properties of this operator, we develop a comprehensive framework to analyze the proposed system. Our findings, established through the application of Schauder's fixed point theorem and the Banach contraction principle, contribute to the understanding of complex phenomena modeled by fractional differential equations. This research expands the boundaries of fractional calculus and offers potential applications in various scientific and engineering domains.

Existence of Fixed Point Theorems in Revised Fuzzy Modular Metric Spaces

Aim of this paper, to established existance of new fixed point theorems in revised fuzzy modular space by deriving variants of Banach contraction principle under the class of inner and outer contractions.

Implementation of the Principles of Agreement (Contact) in Islamic Bank Fund Raising Products

The significant growth of Islamic Banks requires them to be able to meet the needs of the community by offering various products, one of which is a fundraising product that is in accordance with Sharia Principles. In order to raise funds, Islamic Banks provide various forms of financing that have their own contracts/agreements. This study aims to describe and analyze the principles of contracts in Islamic Bank fund raising products. The method used in this research is Library Research, with an analytical descriptive approach to clearly describe the principles of contracts in Islamic Bank fund raising products. The results showed that the principles of contracts in fund-raising products at Islamic Banks have been implemented properly, where the operational activities of Islamic Banks are carried out in accordance with sharia principles supervised by DSN-MUI. Islamic banks provide freedom to customers to choose the type of contract they want without coercion, and guarantee legal equality between the two parties in making the contract. In addition, every agreement made is written and binding, reflecting honesty and freedom in the preparation of contracts between Islamic Banks and customers. The implications of this study show that the implementation of good contract principles in Islamic Banks not only strengthens customer trust but also supports sharia compliance in banking operations. This is important for improving the sustainability and reputation of Islamic Banks in the midst of financial industry competition.

Fixed-Point Theorems Using α-Series in F-Metric Spaces

Fixed-point theory, which has been developing since 1922, is widely used. Various contraction principles have been defined in the literature. In this work, we define rational-type contraction and weak Choudhury type contraction using α-series in F-metric spaces and prove common fixed-point theorems for sequences of self-mappings. This method is based on the convergence series of coefficients. Our results are the generalized version of the results in the literature. Finally, we apply our main results to solve an integral equation and a differential equation.

LEGAL PROTECTION FOR WORKERS AT LKP SAHABAT CENDEKIA SIGLI, INDONESIA

The Institute of Courses and Education or LKP is one form of non-formal education institution that employs educators as applicable in formal education. However, in some LKP cases, it raises problems including the absence of contractual provisions of employment agreements that cause uncertainty and protection for both parties between LKP and workers. For this reason, the focus of this research is how is the system and form of employment contract and its implementation at LKP Sahabat Cendekia Sigli, and how is the legal protection for workers at LKP Sahabat Cendekia Sigli reviewed according to the ijārah ‘alā al-’amal contract? This research is studied with a conceptua lapproach approach with the type of empirical legal research. The result of the research is that the system and form of employment contract between workers and LKP Sahabat Cendekia Sigli is in the form of an oral agreement with the provision that the manager explains the amount of salary/wages per hour and subject, as well as teaching hours or days. The LKP does not explain the expiration date of the contract. In the context of protection and legal certainty, the status of workers in the LKP and the LKP itself does not have legal certainty. On the one hand, there is uncertainty and legal protection for the LKP because workers can decide to resign/leavethe LKP. On the other hand, workers also do not get legal certainty and protection because the LKP can also terminate the employment contract at any time. For this reason, seen from the ijārah ‘ala al-’amal contract, the implementation of the employment contract at the Sahabat Cendekia Sigli LKP is not in accordance with the principles of sharia contracts. The ijārah alā al-'amal contract requires the certainty of a written agreement contract and the actions of the two parties are bound by and limited by the agreed agreement letter. This is what is missing in the work agreement at LKP Sahabat Cendekia Sigli.

The choice of the PICC as the proper law of the contract in Latin American jurisdictions: Chilean contract law as a sample study

Abstract This article analyses a distinctive trend in Latin American conflict laws to enable the parties to choose the Unidroit Principles of International Commercial Contracts (PICC) as the proper law of the contract since this choice must be upheld by national courts. This provides an incentive for contracting parties linked to Latin American jurisdictions to adopt updated and fair rules that are inexistent in their domestic contract laws. This trend began with the 1994 Mexico Convention and has spread to the new conflict rules on contracts enacted in Latin America and even to the 2015 Hague Principles. Nowadays, the choice of the PICC to govern the substance of a contract might be upheld in the national courts of several Latin American countries. This solution is unique since it is not allowed in most jurisdictions, such as those of the European Union, which only accept ‘ordinary legal techniques’ for applying the PICC. There is now legal certainty that the PICC will be applied in arbitration and litigation in these Latin American jurisdictions, either via the ordinary legal techniques or via choosing the PICC as the rules of law governing a contract subject to judicial adjudication. This benefits parties that do not have in their domestic contract law some of the PICC’s solutions. Using Chilean contract law as a sample study, we will show that the PICC’s rules on the pre-contractual stage and on hardship are better suited than existing national laws to negotiate, conclude, and perform international commercial contracts.

Reconciliation at the Border of Public and Private Law: Rethinking Contract Principles in the Context of Impact and Benefit Agreements

Reconciliation at the Border of Public and Private Law: Rethinking Contract Principles in the Context of Impact and Benefit Agreements

Fuzzy Langevin fractional delay differential equations under granular derivative

Analytical studies of the class of the fuzzy Langevin fractional delay differential equations (FLFDDEs) are frequently complex and challenging. It is necessary to construct an effective technique for the solution of FLFDDEs. This article presents an explicit analytical representation of the solution to the class of FLFDDEs with the general fractional orders under granular differentiability. The closed-form solution to the FLFDDEs is extracted for both the homogeneous and non-homogeneous cases using the Laplace transform technique and presented in terms of the delayed Mittag-Leffler type function with double infinite series. Moreover, the existence and uniqueness of the solutions of the FLFDDEs are investigated using the generalized contraction principle. An illustrative example is provided to support the proposed technique. To add to the originality of the presented work, the FLFDDEs with constant delay are solved by applying vibration theory and visualizing their graphs to support the theoretical results.

Sustainable development clauses in international contracts through the lens of the Unidroit principles

Abstract Most transactions that leave an imprint on the environment and communities are organized by commercial contracts. However, little is known about the way in which parties reflect sustainable development in contractual clauses. How can parties to international contracts commit to respect sustainable development goals? What are the possible degrees of commitment? Which contractual mechanisms can apply to the monitoring of compliance? How does one establish a link between the failure to meet sustainable development goals and the contractual liability or termination of contract? This article identifies contractual clauses relating to sustainable development and analyses these clauses through the lens of the 2016 International Institute for the Unification of Private Law (Unidroit) Principles of International Commercial Contracts (PICC). Drawing inspiration from open access contracts, the analysis will demonstrate that Article 1.8 of the PICC, precluding inconsistent behaviour, and Articles 5.1.4 and 5.1.5, on the duty of best efforts and the obligation to achieve a specific result, as well as the provisions on liability, can assist contract drafters, judges, and arbitrators in drafting and interpreting such clauses.

Exploring existence, uniqueness, and stability in nonlinear fractional boundary value problems with three-point boundary conditions

This study investigates the analysis of the existence, uniqueness, and stability of solutions for a Ψ-Caputo three-point nonlinear fractional boundary value problem using the Banach contraction principle and Sadovskii’s fixed point theorem. We demonstrate the practical implications of our analytical advancements for each situation, illustrating how the components of the fractional boundary value problem emerge in real-life occurrences. Our work significantly enhances the field of applied mathematics by offering analytical solutions and valuable insights.

Nonlinear Contractions Employing Digraphs and Comparison Functions with an Application to Singular Fractional Differential Equations

After the initiation of Jachymski’s contraction principle via digraph, the area of metric fixed point theory has attracted much attention. A number of outcomes on fixed points in the context of graph metric space employing various types of contractions have been investigated. The aim of this paper is to investigate some fixed point theorems for a class of nonlinear contractions in a metric space endued with a transitive digraph. The outcomes presented herewith improve, extend and enrich several existing results. Employing our findings, we describe the existence and uniqueness of a singular fractional boundary value problem.

Existence, Uniqueness, and Stability of a Nonlinear Tripled Fractional Order Differential System

This manuscript investigates the existence, uniqueness, and different forms of Ulam stability for a system of three coupled differential equations involving the Riemann–Liouville (RL) fractional operator. The Leray–Schauder alternative is employed to confirm the existence of solutions, while the Banach contraction principle is used to establish their uniqueness. Stability conditions are derived utilizing classical nonlinear functional analysis techniques. Theoretical findings are illustrated with an example. The proposed system generalizes third-order ordinary differential equations (ODEs) with different boundary conditions (BCs).

Analysis of Non-Local Integro-Differential Equations with Hadamard Fractional Derivatives: Existence, Uniqueness, and Stability in the Context of RLC Models

In this study, we focus on the stability analysis of the RLC model by employing differential equations with Hadamard fractional derivatives. We prove the existence and uniqueness of solutions using Banach’s contraction principle and Schaefer’s fixed point theorem. To facilitate our key conclusions, we convert the problem into an equivalent integro-differential equation. Additionally, we explore several versions of Ulam’s stability findings. Two numerical examples are provided to illustrate the applications of our main results. We also observe that modifications to the Hadamard fractional derivative lead to asymmetric outcomes. The study concludes with an applied example demonstrating the existence results derived from Schaefer’s fixed point theorem. These findings represent novel contributions to the literature on this topic, significantly advancing our understanding.

The Banach Fixed Point Theorem: selected topics from its hundred-year history

On June 24, 1920 Stefan Banach presented his doctoral dissertation titled O operacjach na zbiorach abstrakcyjnych i ich zastosowaniach do równañ całkowych (On operations on abstract sets and their applications to integral equations) to the Philosophy Faculty of Jan Kazimierz University in Lvov. He passed his PhD examinations in mathematics, physics and philosophy, and in January 1921 he became a doctor. A year later, he published the results of his doctorate in Fundamenta Mathematicae. Among them there was the theorem known today as the Banach Fixed Point Theorem or the Banach Contraction Principle. It is one of the most famous theorems in mathematics, one of many under the name of Banach. It concerns certain mappings (called contractions) of a complete metric space into itself and it gives the conditions sufficient for the existence and uniqueness of a fixed point of such mapping. In 2022 we had a centenary of publishing this theorem. In the paper, we want to present its most important modifications and generalizations, several contractive conditions, the converse theorems and some applications. It is not possible to provide complete information about what has been written during the last hundred years about the Banach Fixed Point Theorem and we are just trying to touch on some breakthrough moments in the development of the metric fixed point theory. The main purpose of this article is to organize the knowledge on this subject and to elaborate a broad bibliography which all interested persons can refer to.