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We obtain results on the existence and approximation of fixed points of enriched contractions in quasi-Banach spaces and thus extend the previous results for enriched contractions defined on Banach spaces [Berinde, V.; Păcurar, M. Approximating fixed points of enriched contractions in Banach spaces. J. Fixed Point Theory Appl. 22 (2020), no. 2, Paper No. 38, 10 pp.]. The theoretical results are illustrated by means of an appropriate example of enriched contraction on a quasi-Banach space which is not a Banach space and thus show that our new results are effective generalizations of the previous ones in literature. [ABSTRACT FROM AUTHOR]

The economic landscape of the UK has been significantly shaped by the intertwined issues of Brexit, COVID, and their interconnected impacts. The disruptions caused by Brexit and the COVID pandemic have created uncertainty and upheaval for both businesses and individuals. Whilst the effects of COVID are now receding, Brexit is still dominating headlines seven years after the referendum and is likely to do so for the foreseeable future. In this introduction, we provide an overview of the literature on Brexit. We review the reasons for leaving the European Union, as well examine the consequences of Brexit, with a focus on investment, economic growth, trade, unemployment, and financial markets. We then introduce the seven papers selected from the 'Post Brexit: Uncertainty, Risk Measurement and Coronavirus Challenges Conference' held at Birmingham Business School in June 2021, that advance the current literature on the effects of Brexit and COVID on the UK economy. Evidence in these papers suggests that Brexit and COVID are still clearly posing a severe strain on the UK's economy. However, some papers suggest that not everything about Brexit has been detrimental, or at least certain sectors of the UK economy are displaying a marked resilience. [ABSTRACT FROM AUTHOR]

This paper presents the design and construction of a small-scale low-speed open circuit wind tunnel suitable for experimental testing and analysis of aerodynamic phenomena. The wind tunnel is specifically designed for low-speed applications, focusing on flows within velocities of 35 meters per second with turbulence conditions below 10 percent. The design process of a wind tunnel involves considerations such as dimensions, design parameters, and instrumentation to ensure accurate flow measurements, with key components including a settling chamber, contraction section, test section, diffuser, and drive system working together to remove disturbances, create uniform flow, minimize blockage effects, and generate required airflow for accurate aerodynamic testing. This paper highlights the design considerations, key components, construction techniques, and the significance of the wind tunnel for aerodynamic testing, validation of simulations, and education. The designed wind tunnel is capable of producing controlled and repeatable low-speed flow conditions, making it suitable for a wide range of applications, including aerodynamic testing of scaled-down models, validation of Computational Fluid Dynamics (CFD) simulations, and educational purposes. The small-scale design allows for cost-effective construction and operation while maintaining reliable results. [ABSTRACT FROM AUTHOR]

The rationale of this work is to introduce the notion of graphical symmetric spaces and some fixed-point results are proved for H - (ϑ , φ) -contractions in this setting. The idea of graphical symmetric spaces generalizes various spaces equipped with a function which characterizes the distance between two points of the space. Some topological properties of graphical symmetric spaces are discussed. Some fixed-point results for the mappings defined on graphical symmetric spaces are proved. The fixed-point results of this paper generalize and extend several fixed-point results in this new setting. The main results of this paper are applied to obtain the positive solutions of fractional periodic boundary value problems. [ABSTRACT FROM AUTHOR]

The technique to broaden the scope of fixed point theory is to extend the class of spaces that have stronger conceptual frameworks than metric spaces. Therefore, this paper explores the introduction of novel metric spaces, namely, Branciari suprametric spaces, and investigates some of its fundamental topological properties. An illustration is provided to validate the newly defined idea of Branciari suprametric spaces. Further two intriguing, fixed point results are proved, and a corollary is presented as an implication of our main result. The following is a specification of the analogue of the rectangle inequality in Branciari suprametric spaces dB (τ,ι) ≤ dB (τ,ν)+dB(ν,σ)+dB(σ,ι) + μdB (τ,ν)dB(ν,σ)dB(σ,ι) for all t≠v, v≠σ and σ≠1. Furthermore, by employing the results obtained, the present study intends to provide an appropriate solution for the nonlinear fractional differential equations of the RiemannLiouville type. [ABSTRACT FROM AUTHOR]

In this paper we prove new fixed point results in partially ordered bicomplete quasimetric spaces. Our results extends/generalized celebrated results, on the one hand, by Nieto and Rodríguez-López for contraction mappings in partially ordered complete metric spaces and, on the other hand, by Schellekens for contraction mappings in bicomplete quasi-metric spaces. Moreover, it is also shown that neither our assumptions can be weakened nor our results can be deduced from the celebrated Kleene's fixed point theorem. Finally, an application of our results to the asymptotic analysis of recurrence equations is given. [ABSTRACT FROM AUTHOR]

In the present paper, we obtain three results on the existence of a fixed point for nonexpansive mappings. Two of them are generalizations of the result for F-contraction, while third one is a generalization of a recent result for set-valued contractions. [ABSTRACT FROM AUTHOR]

Two of the most well-known belief contraction operators are partial meet contractions (PMCs) and kernel contractions (KCs). In this paper we propose two new classes of contraction operators, namely the class of generalized partial meet contractions (GPMC) and the class of generalized kernel contractions (GKC), which strictly contain the classes of PMCs and of KCs, respectively. We identify some extra conditions that can be added to the definitions of GPMCs and of GKCs, which give rise to some interesting subclasses of those classes of functions, namely the classes of extensional and of uniform GPMCs/GKCs. In the context of contractions on belief sets the classes of partial meet contractions, uniform GPMCs and extensional GPMCs are all identical. Nevertheless, when considered as operations on belief bases, the class of uniform GPMCs coincides with the class of partial meet contractions, but the extensional GPMCs constitute a new kind of belief base contraction functions whose characterizing postulate of irrelevance of syntax is extensionality—the same postulate of irrelevance of syntax which occurs in the classical axiomatic characterization of partial meet contractions for belief sets—rather than the postulate of uniformity—which is the irrelevance of syntax postulate used in the axiomatic characterization for partial meet contractions on belief bases. Analogous results are obtained regarding the classes of extensional and of uniform GKCs. We present the interrelations in the sense of inclusion among all the new classes of operators presented in this paper and several well known classes of PMCs and of KCs. [ABSTRACT FROM AUTHOR]

In this paper, we investigate several new classes of multi-dimensional almost automorphic type sequences and focus on their applications to various difference equations involving Volterra difference equations. We provide many structural results, illustrative examples and open problems about the notion under consideration. [ABSTRACT FROM AUTHOR]

Let G = (V , E) be a simple graph. A dominating set of G is a subset S ⊆ V such that every vertex not in S is adjacent to at least one vertex in S. The cardinality of a smallest dominating set of G , denoted by γ (G) , is the domination number of G. A dominating set S is called a super dominating set of G , if for every vertex u ∈ S ¯ = V − S , there exists v ∈ S such that N (v) ∩ S ¯ = { u }. The cardinality of a smallest super dominating set of G , denoted by γ sp (G) , is the super domination number of G. In this paper, we study super domination number of some graph classes and present sharp bounds for some graph operations. [ABSTRACT FROM AUTHOR]

The paper analyses the local well posedness of the initial value problem for the k-generalized Korteweg-de Vries equation for k = 3 with irregular initial data. k-generalized Korteweg-de Vries equations serve as a model of magnetoacoustic waves in plasma physics, of the nonlinear propagation of pulses in optical fibers. The solvability of many dispersive nonlinear equations has been studied in weighted Sobolev spaces in order to manage the decay at infinity of the solutions. We aim to extend these researches to the k-generalized KdV with k = 3. For initial data in classical Sobolev spaces there are many results in the literature for several nonlinear partial differential equations. However, our main interest is to investigate the situation for initial data in Sobolev weighted spaces, which is less understood. The low regularity Sobolev results for initial value problems for this dispersive equation was established in unweighted Sobolev spaces with s ≥ 1/12 and later further improved for s ≥ -1/6. The paper improves these results for 3-KdV equation with initial data from weighted Sobolev spaces. [ABSTRACT FROM AUTHOR]

In this paper, the concepts of Wardowski-type set-valued contractions and Işik-type set-valued contractions are introduced and fixed point theorems for such contractions are established. A positive answer to the open Question is given. Examples to support main theorems and an application to integral inclusion are given. [ABSTRACT FROM AUTHOR]

Most artificial muscles currently in existence driven by negative pressure are in the form of origami. Their contractions are directly attained by extracting the air internal, and obtaining a differential pressure with the external (0.101 MPa). During contraction, the artificial muscle simultaneously encounters radial and axial pressures provided by the atmosphere. If the muscle is isotropic, the radial pressure would make the artificial muscle unreliable, which would weaken the muscle's contraction, including contraction force, ratio, and speed. This paper first introduces the contraction theory and dysfunction of the muscle. Then, an optimization method is proposed as local reinforcement, aiming at the muscle's dysfunction that may occur during contraction. Then, by analyzing and comparing the optimization effects on the muscle contraction force and deformation with different reinforced regions, the endplates and crests are determined to be appropriate. Subsequently, the deformations of the reinforced regions when stressed are analyzed, and the adequate reinforcement dimensions are confirmed. Finally, the muscle's model passes the simulation for ensuring its contraction without dysfunction, demonstrating the rationality of the reinforcement method proposed in this paper. Hereby, the goal of reinforcing the muscle's radial stiffness is achieved, making the artificial muscle generate an optimal contraction performance. [ABSTRACT FROM AUTHOR]

This paper models the cyber-social system as a cyber-network of agents monitoring states of individuals in a social network. The state of each individual is represented by a social node, and the interactions among individuals are represented by a social link. In the cyber-network, each node represents an agent, and the links represent information sharing among agents. The agents make an observation of social states and perform distributed inference. In this direction, the contribution of this paper is threefold: First, a novel distributed inference protocol is proposed that makes no assumption on the rank of the underlying social system. This is significant as most protocols in the literature only work on full-rank systems. Second, a novel agent classification is developed, where it is shown that the connectivity requirement of the cyber-network differs for each type. This is particularly important in finding the minimal number of observations and minimal connectivity of the cyber-network as the next contribution. Third, the cost-optimal design of the cyber-network constraint with distributed observability is addressed. This problem is subdivided into sensing cost optimization and networking cost optimization, where both are claimed to be NP-hard. We solve both the problems for certain types of social networks and find polynomial-order solutions. [ABSTRACT FROM AUTHOR]

The aim of this research paper is to extend the results of Karapinar and Khojasteh [13], Karapinar and Fulga [12] in super metric space by using weakly compatible mappings. Further, the analogue results of Jungck[10], Das and Naik [6], and Ciric [5] in quasi-contraction mappings are generalized in super metric space. [ABSTRACT FROM AUTHOR]

In the present paper, we generalize the results of Karapinar and Khojasteh [7], Karapinar and Fulga [6] in super metric space by using the control function and weakly compatible mappings. [ABSTRACT FROM AUTHOR]

The notion of conservative algebras appeared in a paper by Kantor in 1972. Later, he defined the conservative algebra W(n) of all algebras (i.e. bilinear maps) on the n-dimensional vector space. If n > 1, then the algebra W(n) does not belong to any well-known class of algebras (such as associative, Lie, Jordan, or Leibniz algebras). It looks like W(n) in the theory of conservative algebras plays a similar role to the role of 픤픩n in the theory of Lie algebras. Namely, an arbitrary conservative algebra can be obtained from a universal algebra W(n) for some n ∈ ℕ. The present paper is part of a series of papers, which is dedicated to the study of the algebra W(2) and its principal subalgebras. [ABSTRACT FROM AUTHOR]

The authors deal with nonlinear and general Hammerstein-type functional integral equations (HTFIEs). The first objective of this work is to apply and extend Burton's method to general and nonlinear HTFIEs in a Banach space via the Chebyshev norm and complete metric. The second objective of the paper is to extend and improve some earlier results to nonlinear HTFIEs. The authors prove two new theorems with regard to the existence and uniqueness of solutions (EUSs) of HTFIEs via a technique called progressive contractions, which belongs to T. A. Burton, and the Chebyshev norm and complete metric. [ABSTRACT FROM AUTHOR]

Given a permutation σ on n symbols { 0 , 1 , ... , n - 1 } and an integer 1 ≤ m ≤ n - 1 , the mth contraction of σ is the permutation σ CT m on n - m symbols obtained by deleting the symbols n - 1 , n - 2 , ... , n - m from the cycle decomposition of σ . The Hamming distance hd (σ , τ) between two permutations σ and τ is the number of symbols x such that σ (x) ≠ τ (x) . In this paper we give a complete characterization of the effect of a single contraction on the Hamming distance between two permutations. This allows us to obtain sufficient conditions for hd (σ , τ) - hd (σ CT m , τ CT m) ≤ 2 m . [ABSTRACT FROM AUTHOR]

In this paper we work in the category of approach spaces with contractions [14], the objects of which are sets endowed with a numerical distance between sets and points. Approach spaces are to be considered a simultaneous generalization of both quasi-metric and topological spaces. Especially the fundamental notion of distance is reminiscent of the closure operator in a topological space and of the point-to-set distance in a quasi-metric space. The embedding of the category of topological spaces with continuous maps and of quasi-metric spaces with non-expansive maps is extremely nice. Every approach space has both a quasi-metric coreflection as well as a topological coreflection. Different approach spaces though can have the same topological as well as the same quasi-metric coreflection, in other words, in general these coreflections do not determine the approach space. In this paper we investigate approach spaces for which these coreflections, do determine the approach space. We will call such spaces supported. We prove that in the setting of compact approach spaces many examples of supported approach spaces can be found. Thus, compact spaces that are base-regular, which is a weakening of regularity, are always supported. An important feature of supported approach spaces is the behaviour of contractions. On a supported domain contractivity is characterized by the combination of continuity for the topological coreflection and non-expansiveness for the quasi-metric coreflection. This result implies that a supported approach space actually is the infimum of its quasi-metric and its topological coreflection. In the course of our study we also give several more examples of both supported and non-supported approach spaces. [ABSTRACT FROM AUTHOR]

In this paper, we consider a planar viscous shock of moderate strength for a scalar viscous conservation law in multi-D. We consider a strictly convex flux, as a small perturbation of the Burgers flux, along the normal direction to the shock front. However, for the transversal directions, we do not have any restrictions on flux function. We first show the contraction property for any large perturbations in L2 of the planar viscous shock. If the initial L2-perturbation is also in L1, the large perturbation converges to zero in L2 as time goes to infinity with t−1/4 decay rate. The contraction and decay estimates hold up to dynamical shift. For the results, we do not impose any smallness conditions on the initial value. This result extends the 1D case [M.-J. Kang and A. F. Vasseur, L2-contraction for shock waves of scalar viscous conservation laws, Ann. Inst. H. Poincaré C Anal. Non Linéaire 34 (2017) 139–156] by the first author and Vasseur to the multi-dimensional case. [ABSTRACT FROM AUTHOR]

The monotone variational inequalities are being widely used as mathematical tools for studying optimal control problems and convex programming. In this paper, we propose a new prediction-correction method for monotone variational inequalities with linear constraints. The method consists of two procedures. The first procedure (prediction) utilizes projections to generate a predictor. The second procedure (correction) produces the new iteration via some minor computations. The main advantage of the method is that its main computational effort only depends on evaluating the resolvent mapping of the monotone operator, and its primal and dual step sizes can be enlarged. We prove the global convergence of the method. Numerical results are provided to demonstrate the efficiency of the method. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of graphical cone metric spaces over Banach algebra and prove some fixed point results for a particular type of contractive mappings defined on such spaces. These results extend and generalize several results from metric, graphical metric, and cone metric spaces. Some examples that demonstrate the results proved herein are provided. An application of our results to the existence of solution of a pair of initial value problems is provided. [ABSTRACT FROM AUTHOR]

In the present paper we construct a new approach structure called Fell approach structure. We define the new structure by means of lower regular function frames and prove that the Top-coreflection of this new structure is the ordinary Fell topology. We also give analogue result for the extended Fell topology and investigate some properties of Fell approach structure. [ABSTRACT FROM AUTHOR]

The celebrated S-Lemma was originally proposed to ensure the existence of a quadratic Lyapunov function in the Lur'e problem of absolute stability. A quadratic Lyapunov function is, however, nothing else than a squared Euclidean norm on the state space (that is, a norm induced by an inner product). A natural question arises as to whether squared non-Euclidean norms V (x) = ||x|| 2 may serve as Lyapunov functions in stability problems. This paper presents a novel nonpolynomial S-Lemma that leads to constructive criteria for the existence of such functions defined by weighted lp norms. Our generalized S-Lemma leads to new absolute stability and absolute contractivity criteria for Lur'e-type systems, including, for example, a new simple proof of the Aizerman and Kalman conjectures for positive Lur'e systems. [ABSTRACT FROM AUTHOR]

Generally, the field of fixed point theory has attracted the attention of researchers in different fields of science and engineering due to its use in proving the existence and uniqueness of solutions of real-world dynamic models. C*- algebra is being continually used to explain a physical system in quantum field theory and statistical mechanics and has subsequently become an important area of research. The concept of a C*-algebra-valued metric space was introduced in 2014 to generalize the concept of metric space. In fact, It is a generalization by replacing the set of real numbers with a C*-algebra. After that, this line of research continued, where several fixed point results have been obtained in the framework of C*-algebra valued metric, as well as (more general) C*-algebra-valued b-metric spaces and C*-algebra-valued extended b-metric spaces. Very recently, based on the concept and properties of C* -algebras, we have studied the quasi-case of such spaces to give a more general notion of relaxing the triangular inequality in the asymmetric case. In this paper, we first introduce the concept of C*-algebra-valued quasi-controlled K -metric spaces and prove some fixed point theorems that remain valid in this setting. To support our main results, we also furnish some examples which demonstrate the utility of our main result. Finally, as an application, we use our results to prove the existence and uniqueness of the solution to a nonlinear stochastic integral equation. [ABSTRACT FROM AUTHOR]

In this paper, a novel chemo-mechanical model is proposed for the description of the stretch-dependent chemical processes known as Bayliss effect and their impact on the active contraction in vascular smooth muscle. These processes are responsible for the adaptive reaction of arterial walls to changing blood pressure by which the blood vessels actively support the heart in providing sufficient blood supply for varying demands in the supplied tissues. The model is designed to describe two different stretch-dependent mechanisms observed in smooth muscle cells (SMCs): a calcium-dependent and a calcium-independent contraction. For the first one, stretch of the SMCs leads to an inlet of calcium ions which activates the myosin light chain kinase (MLCK). The increased activity of MLCK triggers the contractile units of the cells resulting in the contraction on a comparatively short time scale. For the calcium-independent contraction mechanism, stretch-dependent receptors of the cell membrane stimulate an intracellular reaction leading to an inhibition of the antagonist of MLCK, the myosin light chain phosphatase resulting in a contraction on a comparatively long time scale. An algorithmic framework for the implementation of the model in finite element programs is derived. Based thereon, it is shown that the proposed approach agrees well with experimental data. Furthermore, the individual aspects of the model are analyzed in numerical simulations of idealized arteries subject to internal pressure waves with changing intensities. The simulations show that the proposed model is able to describe the experimentally observed contraction of the artery as a reaction to increased internal pressure, which can be considered a crucial aspect of the regulatory mechanism of muscular arteries. [ABSTRACT FROM AUTHOR]

Primal-dual hybrid gradient (PDHG) method is a canonical and popular prototype for solving saddle point problem (SPP). However, the nonlinear coupling term in SPP excludes the application of PDHG on far-reaching real-world problems. In this paper, following the seminal work by Valkonen (Inverse Problems 30, 2014), we devise a variant iterative scheme for solving SPP with nonlinear function by exerting an alternative extrapolation procedure. The novel iterative scheme falls exactly into the proximal point algorithmic framework without any residuals, which indicates that the associated inclusion problem is "nearer" to the KKT mapping induced by SPP. Under the metrically regular assumption on KKT mapping, we simplify the local convergence of the proposed method on contractive perspective. Numerical simulations on a PDE-constrained nonlinear inverse problem demonstrate the compelling performance of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper we prove Caristi’s fixed point theorem using only purely metric techniques. [ABSTRACT FROM PUBLISHER]

In this research, we have settled some coupled fixed point results with rational contraction in partially ordered b-metric spaces (PObMS). The findings introduced here are generalizations and extensions of some of the established results in the literature. The applications of our result have been discussed in the final section of the paper. [ABSTRACT FROM AUTHOR]

In this paper, we aim to study the neutral-type delayed Caputo fractional differential equations of the form C D α x t − g t , x t = f t , x t , t ∈ t 0 , ∞ , t 0 ≥ 0 with order 0 < α < 1 , which can be used to describe the growth processes in real-life sciences at which the present growth depends on not only the past state but also the past growth rate. Our ultimate goal in this study is to concentrate on the convergence of the solutions to a predetermined constant by establishing a linkage between the delayed fractional differential equation and an integral equation. In our analysis, the sufficient conditions for the asymptotic results are obtained due to fixed point theory. The utilization of the contraction mapping principle is a convenient approach in obtaining technical conditions that guarantee the asymptotic constancy of the solutions. [ABSTRACT FROM AUTHOR]

Fixed point iterations of some contraction mappings with variations in cone metric space (CMS) domains have been discussed in this paper. More specifically, an increasing sequence of subsets of an order complete CMSs has been considered such that one member of the sequence is mapped into the next member of the sequence by a map for which a contraction condition is satisfied. The usual iteration method has been considered to establish generalized fixed point results in CMSs. Furthermore, some examples are provided to illustrate our main results. [ABSTRACT FROM AUTHOR]

One of the important consequences of the Banach fixed point theorem is Hutchinson's theorem which states the existence and uniqueness of fractals in complete metric spaces. The aim of this paper is to extend this theorem for semimetric spaces using the results of Bessenyei and Páles published in 2017. In doing so, some properties of semimetric spaces as well as of the fractal space are investigated. We extend Hausdorff's theorem to characterize compactness and Blaschke's theorems to characterize the completeness of the fractal space. Based on these preliminaries, an analogue of Hutchinson's theorem in the setting of semimetric spaces is proved, and finally, error estimates and stability of fractals are established as well. [ABSTRACT FROM AUTHOR]

Cemented paste backfill (CPB) plays an increasingly important role in the mining industry due to its operational and environmental benefits. CPB is placed in the mined-out stope to form a self-supporting structure. The strength and stability of the CPB is of great concern in its engineering applications. Indeed, CPB must remain stable during the extraction of adjacent stopes to ensure the safety of the mine operations. Although significant research has been conducted on the shear properties of CPB, there are limited studies on its post-failure behavior, in particular the yield characteristics of CPB. This paper presents the finding on the post-peak and yield property of CPB. The study is conducted on three cemented contents and six stress intervals based on the mining practice and field study. The results show that CPB exhibits dilative behavior under strain softening and contractive property under strain hardening conditions. Our study demonstrates that pure frictional resistance could exceed the cohesion strength at high stress levels. [ABSTRACT FROM AUTHOR]

In this paper, we define enriched (ψ, φλ)-weakly contractive map in convex metric spaces where ψ is continuous on [0,+∞) and φλ is not continuous on [0,+∞) and prove the existence and uniqueness of fixed points of these maps in complete convex metric spaces. We provide an example in support of our result. [ABSTRACT FROM AUTHOR]