Generalized Contraction Principle Research Articles

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.

Stability analysis for complex-valued neural networks with fractional order

In the context of complex-valued rectangular b-metric spaces, the present study investigates the stability of complex-valued neural networks (CVNNs) with fractional order. Using the generalized contraction principle, we address the suitable condition for uniform stability of fractionally ordered CVNNs and establish the existence and uniqueness of the equilibrium point. Few numerical results are presented to show the feasibility and correctness of the results presented.

Contract and Aqd, are they functionally different?

PurposeThe purpose of this paper is to determine whether there is any fundamental difference in the meaning of contract in these two legal systems by analysing some of the essential principles of contract particularly parties’ agreement and consideration.Design/methodology/approachThis paper seeks to investigate the degree of equivalency of the term contract and its Islamic law counterpart “Aqd”. To implement this task, it applies some comparative law techniques to examine certain contractual elements under common law and Islamic law.FindingsThe argument that “contract” and “Aqd” are not equivalent is superficial, and it is not well-supported by concrete evidence. The examples used to build this argument are merely limited exceptions to the general principles of contract, and some of them even exist under both legal systems in a similar manner such as “deed” and “Hibah”.Practical implicationsThe paper is of interest to legal practitioners and professionals working in cross-cultural or international contexts, as understanding points of conformity and disconformity between “contract” and “Aqd” can help in multiple ways. These may include negotiating international transactions, contract drafting and dispute-resolution processes involving parties from Western and Islamic law-based jurisdictions. It may also aid policymaking and lawmaking processes aiming to harmonize contract principles across different jurisdictions.Social implicationsThe research paper is important for public attitude, as understanding similarities and differences between “contract” and “Aqd” fosters mutual respect, tolerance and cooperation between individuals and communities adhering to different legal systems.Originality/valueThere is a common belief that the term “contract” substantially differs from “Aqd”, and it is by no means safe to presume that every “Aqd” qualifies as a contract. The current research introduces a new point view on the degree of conceptual equivalency of the two terms by showing resemblances in aspects relating to some contractual elements which have always been viewed as an area of divergence rather than convergence.

The fuzzy fractional SIQR model of computer virus propagation in wireless sensor network using Caputo Atangana–Baleanu derivatives

This work is devoted to study the uncertain attacking behavior of computer viruses in wireless sensor network involving fuzzy fractional derivatives with non-local Mittag-Leffler function kernel. Based on epidemic theory and fractional calculus, we propose a fuzzy fractional Susceptible – Infectious – Quarantine – Recovered (SIQR) model to describe dynamics of virus propagation with quarantine in the network. The concept of Atangana–Baleanu fuzzy fractional derivative in Caputo sense is proposed with some important properties to investigate the fractional SIQR model with fuzzy data. The fuzzy Laplace transform of Atangana–Baleanu derivative is proposed to represent the analytic mild solutions of the fractional SIQR model. Then, the existence and uniqueness of mild solutions is proved by using generalized contraction principle. An efficient numerical scheme to solve numerical solutions of the fractional SIQR model is introduced. Finally, some graphical representations are given to show the uncertain attack behavior of computer virus and dynamical behavior of the model.

Cyber insurance – What coverage in case of an alleged act of War? Questions raised by the Mondelez v. Zurich case

In October 2018, snack company Mondelez International, Inc. (Mondelez) filed an action against Zurich American Insurance Company (Zurich), requesting indemnification for more than USD $100,000,000 in losses caused by the NotPetya cyber virus. Zurich refuses to cover these damages alleging one of the insurance policy's exclusions for damage resulting from a hostile or warlike action by a government, as the NotPetya attack is said to have been sponsored by Russia. This case is noteworthy for multiple reasons: not only is it the first significant legal dispute in the insurance field concerning the recovery of costs resulting from a cyber attack, but it is also the first time that an insurance company is invoking the war exclusion to decline coverage for an allegedly state-sponsored cyber hack.This article analyzes the key issues of this important case, including attribution of a cyber attack to a State and interpretation of an insurance policy's war exclusion in a cyber context, and the likelihood of success of Mondelez's arguments. It also explores the strengths and limits of general principles of contract and public international law when applied to new technologies and cyber incidents. Finally, it discusses the potential impacts of the Mondelez case on the contents and limits of future traditional and cyber-specific insurance policies.

Generalized contraction principle under relatively weaker contraction in partial metric spaces

In this paper, we introduce the concept of a generalized weak (phi,mathcal{R})-contraction and employ this to prove some fixed point results for self-mappings in partial metric spaces endowed with a binary relation mathcal{R}. We also establish some consequences in ordered partial metric spaces and metric spaces with a binary relation and exemplify that our results are a sharpened version of results of Zhiqun Xue (Nonlinear Funct. Anal. Appl. 21(3):497–500, 2016) and Alam and Imdad (J. Fixed Point Theory Appl. 17(4):693–702, 2015). Finally, we provide the existence of a solution for integral and fuzzy partial differential equations.

A Generalized Contraction Principle Under w-Distance for a Partially Ordered Metric Space

Fixed point results for generalized weak contractions under w-distance are proved using discontinuous control functions that are more relaxed than functions used in related work for metric spaces. Later, we apply our theory to coupled coincidence point problems and existence of solution of Fredholm type integral equation. We present examples to justify our claims.

Generalized Contraction Principle in Complex valued Metric spaces

In this paper, we introduce the notion of Generalized contractive type mappings in complex valued metric space and establish fixed point theorem for these mappings.

Banach contraction principle for cyclical mappings on partial metric spaces

We prove that the Banacah contraction principle proved by Matthews in 1994 on 0-complete partial metric spaces can be extended to cyclical mappings. However, the generalized contraction principle proved by (Ilic et al. in Appl. Math. Lett. 24:1326-1330, 2011) on complete partial metric spaces can not be extended for cyclical mappings. Some examples are given to illustrate our results. Moreover, our results generalize some of the results obtained by (Kirk et al. in Fixed Point Theory 4(1):79-89, 2003). An Edelstein type theorem is also extended when one of the sets in the cyclic decomposition is 0-compact.

A generalized contraction principle with control functions on partial metric spaces

Partial metric spaces were introduced by Matthews in 1994 as a part of the study of denotational semantics of data flow networks. In this article, we prove a generalized contraction principle with control functions ϕ and ψ on partial metric spaces. The theorems we prove generalize many previously obtained results. We also give some examples showing that our theorems are indeed proper extensions.

A generalized contraction principle in partial metric spaces

In this paper, we prove fixed point theorems for generally contractive mappings in complete partial metric spaces. Theorems presented are generalizations of recent fixed point theorems of D. Ilić, V. Pavlović, and V. Rakocević. An example is also stated that illustrates our results are extensions of their theorems.

Fixed Point for Weakly Compatible Maps Satisfying Generalized Contraction Principle

We prove common fixed point theorems for a pair of weakly compatible mappings satisfying a generalized contraction principle by using a control function and implicit relation. We also establish invariant approximation result as an application of the result.Keywords: Common fixed point; Weakly compatible maps; Control function; Invariant approximation.© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi:10.3329/jsr.v3i3.6476 J. Sci. Res. 3 (3), 549-555 (2011)

Common Fixed Point and Invariant Approximation Theorems for Mappings Satisfying Generalized Contraction Principle

We prove common fixed point theorems for weakly compatible mappings satisfying a generalized contraction principle by using a control function. As an application, we have established invariant approximation result. Our theorems generalize recent results existing in the literature.

Multidimensional version of M. A. Krasnoseľskii’s generalized contraction principle

Let M be a complete K-metric space with n-dimensional metric ρ(x, y): M × M → R n , where K is the cone of nonnegative vectors in R n . A mapping F: M → M is called a Q-contraction if ρ (Fx,Fy) ⩽ Qρ (x,y), where Q: K → K is a semi-additive absolutely stable mapping. A Q-contraction always has a unique fixed point x* in M, and ρ(x*,a) ⩽ (I - Q)-1 ρ(Fa, a) for every point a in M. The point x* can be obtained by the successive approximation method x k = Fx k-1, k = 1, 2,..., starting from an arbitrary point x 0 in M, and the following error estimates hold: ρ (x*, x k ) ⩽ Q k (I - Q)-1ρ(x 1, x 0) ⩽ (I - Q)-1 Q k ρ(x 1, x 0), k = 1, 2,.... Generally the mappings (I - Q)-1 and Q k do not commute. For n = 1, the result is close to M. A. Krasnosel’skii’s generalized contraction principle.

Indoor air quality and the law in Singapore.

With the greater use of air-conditioned offices in Singapore, achieving good indoor air quality has become an important issue. The laws that impose duties upon designers and contractors with respect to the design and construction of air-conditioning and mechanical ventilation (ACMV) systems are set out in the Building Control Regulations and the Singapore Standard Code of Practice for Mechanical Ventilation and Air-conditioning in Buildings (hereinafter "SS CP 13:1980"). ACMV maintenance is governed by the Environmental Public Health Act, the Building and Common Property (Maintenance and Management) Act, and the Land Titles (Strata) Act, as well as by lease or tenancy agreements. Designers, contractors, developers, building owners and management corporations may also be liable to the workers, occupants and other premises users for indoor air quality (IAQ)-related injuries under the general principles of contract and tort. Recently, the Guidelines for Good Indoor Air Quality in Office Premises was issued by the Ministry of Environment to complement SS CP 13:1980 toward improving the indoor air quality of air-conditioned office premises. Although the Guidelines have no statutory effect, they may be adopted as contractual requirements in construction, lease and maintenance contracts. They may also be used to determine the relevant standard of duty of care required to discharge tortious liability. This paper looks at the existing laws and rules affecting the design, construction and maintenance of air-conditioned offices in light of Part III of the Ministry's Guidelines.

Is Silence Still Golden? Misrepresentations in Land Dealings and The Trade Practices Act 1974 (Cwth)

For the legal purist whose craft is distilling principles through the application of the doctrine of precedent, the appearance of an all embracing statute supplanting the common law is never a very welcome sight. It takes many years for such a statute to find a comfortable residence alongside the principles of the common law which it has modified or even virtually destroyed. Such a statute is the Trade Practices Act 1974 (Cwth). By way of analogy, it was not until 1934 that the High Court1 eventually faced up to the concept of immediate indefeasibility of registered title, cases still being argued on the basis of the principles that existed under the old deeds system. The Torrens System was about 80 years old by then. One wonders, even given the innate conservatism of the law, what might be left of general principles of contract after 80 years of the Trade Practices Act 1974 (Cwth).

General Principles of Contract

The following parts of the National Credit Act 34 of 2005 came into operation during 2006 (GN 22 GG 28824 of 11 May 2006) : chap 1 (interpretation, purpose and the application of the Act); chap 2 (establishment of the National Credit Regulator and the National Consumer Tribunal); chap 3 (registration and regulation of credit providers, credit bureaux and debt counsellors); chap 4 part B excluding s 71 (regulation of collection and dissemination of consumer credit information); chap 7 (alternative dispute resolution, as well as investigation and hearings of complaints by the Regulator and Tribunal); chap 8 (powers of search, offences in terms of the Act and miscellaneous matters); and chap 9 (conflicting legislation and transitional arrangements).

Generalized contraction principle

Fixed point theorems are proved for contraction maps on M‐convex spaces.

Remarks on the generalized contraction principle

Remarks on the generalized contraction principle

A generalized contraction principle

This paper presents an extension of Banach's contraction mapping principle to Hausdorff spaces, in fact to the larger class of topological spaces in which convergent sequences have unique limits. This is achieved by considering topologies on X generated by families of quasi-pseudo-metrics on X. An extension of the concept of Cauchy sequence to this non-metric setting is given.