Expansive Mappings Research Articles

A Theorem on k-Expansive Mapping and its Fixed Point in G𝐽 𝑆 – Metric Space

Objectives: To find a fixed point of k-expansive mapping on GJS-metric space by establishing a theorem on it and to prove the uniqueness of such a fixed point. Methods: A theorem for the k-expansive map on GJS-metric space is established by generalizing an existing contractive condition theorem. Generalization is done by replacing the contractive condition with an expansive type of condition. Findings: Certain conditions that have to be satisfied by a k-expansive mapping for the existence and uniqueness of fixed points in GJS-metric space were found in this article. An example is also given to illustrate the existence of a fixed point. Novelty: GJS-metric space is a new metric space that has been established recently. Furthermore, the fixed point theorem of k-expansive mapping on GJS - metric space has not yet been proved by anyone, and hence it is proved in this article. 2020 Mathematics Subject Classification: 47H10, 54H25. Keywords: GJS-Metric space; Symmetric GJS-Metric space; GJS-Continuous function; GJS-Cauchy sequence; Expansive mapping; k-Expansive mapping

Trajectories of Public Islam: Public Religious Expressions among American Muslim Advocates

Abstract In American mainstream cultural discourse, Islam is often constructed as undemocratic, violent, and un-American. How do American Muslim advocates react to these tarnished representations of their religion? This paper examines the ways in which Muslim advocates construct public discourse around Islam by exploring the possibilities for and recognizing the constraints on their public religious expressions in U.S. civic life as advocates navigate cultural templates infused with de-sacralized Christian meanings. Based on participant observation in two Muslim advocacy organizations, the article demonstrates that advocates map Islam differently, depending on whether the imagined audience of their public discourse is other Muslims or non-Muslims. When advocates imagine addressing non-Muslims, the public discourse of both groups similarly emphasizes Islamic compatibility of Muslim with American values. Among both groups, there is a process of filtering certain religious expressions for more expansive social maps that uncovers the unequal power dynamics shaping trajectories of public religion in civic life for one of the most stigmatized ethno-religious groups in the United States today. This paper contributes to expanding our understanding of how civic culture enables and constrains historically marginalized groups’ attempts at redefining belonging.

EDMD for expanding circle maps and their complex perturbations

We show that spectral data of the Koopman operator arising from an analytic expanding circle map τ can be effectively calculated using an EDMD-type algorithm combining a collocation method of order m with a Galerkin method of order n. The main result is that if m≥δn, where δ is an explicitly given positive number quantifying by how much τ expands concentric annuli containing the unit circle, then the method converges and approximates the spectrum of the Koopman operator, taken to be acting on a space of analytic hyperfunctions, exponentially fast in n. Additionally, these results extend to more general expansive maps on suitable annuli containing the unit circle.

Generalized expansive mapping, equiexpansive mapping in $$C^{*}$$-algebra valued metric space and some fixed points results

Generalized expansive mapping, equiexpansive mapping in $$C^{*}$$-algebra valued metric space and some fixed points results

Fixed-Points of Expansive Mappings in Supermetric Spaces

In the present research paper, we prove some fixed-point results for expansive mappings in the framework of super metric space.

Highly Non-contractive Iterated Function Systems on Euclidean Space Can Have an Attractor

AbstractIterated function systems (IFSs) and their attractors have been central to the theory of fractal geometry almost from its inception. Moreover, contractivity of the functions in the IFS has been central to the theory of iterated functions systems. If the functions in the IFS are contractions, then the IFS is guaranteed to have a unique attractor. The converse question, does the existence of an attractor imply that the IFS is contractive, originates in a 1959 work by Bessaga which proves a converse to the contraction mapping theorem. Although a converse is true in that case, it is known that it does not always hold for an IFS. In general, there do exist IFSs with attractors and which are not contractive. However, in the context of IFSs in Euclidean space, this question has been open. In this paper we show that a highly non-contractive iterated function system in Euclidean space can have an attractor. In order to do that, we introduce the concept of an L-expansive map, i.e., a map that has Lipschitz constant strictly greater than one under any remetrization. This is necessitated by the absence of positively expansive maps on the interval.

Common Fixed-Point Theorem for Expansive Mappings in Dualistic Partial Metric Spaces

O'Neill [1] introduces the concept of dualistic partial metric space. In this study, we prove some common fixed-point theorems for dualistic expanding mappings defined on a dualistic partial metric space. Some famous conclusions of [2] and [3] are extended and generalized by our result. Additionally, we offer an example that demonstrates the value of these dualistic expanding mappings.

COMMON FIXED-POINT THEOREMS FOR EXPANSIVE MAPPINGS IN PARAMETRIC METRIC SPACES

In this paper, we establish some common fixed-point results in parametric metric spaces for pairs of expansive mappings. As a result, several findings from metric spaces are expanded to include this additional context. We also provide an example that shows the usefulness of these contractions.

Fixed Point Theorems for \((\xi,\alpha)\)-Expansive Mappings in Metric Like Spaces

Fixed Point Theorems for \((\xi,\alpha)\)-Expansive Mappings in Metric Like Spaces

Existence and Uniqueness of a Second Order Difference Equation of Accretive Type in 2-Banach Spaces

In this paper, we investigate the existence and uniqueness of solutions to a homogeneous second order difference inclusion of accretive type in 2-Banach spaces using expansive mappings and 2-Banach contraction mapping.

Semiring isomorphisms between rational function semifields of tropical curves

We prove that a semiring isomorphism between the rational function semifields of two tropical curves induces an expansive map between those tropical curves. This semiring isomorphism and the expansive map respect zeros and poles of rational functions with their degrees. As a corollary, we show that the automorphism group of a tropical curve is isomorphic to the T-algebra automorphism group of its rational function semifield, where T:=(R∪{−∞},max,+) is the tropical semifield. Finally, we describe all semiring automorphisms of rational function semifields of all tropical curves.

New Fixed Point Theorem for Expansive Maps on a Two – Metric Space

In this paper new theorems a bout fixed point are given for applications in 2- metric space. The common fixed points of two operators exhibit a shared periodicity in their occurrences. The theorem demonstrates that, certain conditions, there exists a specific pattern or sequence of operators where the fixed points exhibit a common periodicity.

Gromov–Hausdorff variational principles and measure stability * *KL and CAM were partially supported by Basic Science Research Program through the NRF funded by the Ministry of Education of the Republic of Korea (Grant Number: 2022R1l1A3053628).

Variational formulae for the Gromov–Hausdorff distances of compact metric spaces and their continuous maps are obtained. Also, a notion of µ-topological GH-stability on metric-measure spaces with probability µ is given. We prove that every expansive map with the weak µ-shadowing property (Lee and Rojas 2022 Russ. J. Nonlinear Dyn. 18 297–307) is µ-topologically GH-stable.

A New faster Iteration Process to fixed points of mean-non expansive Mappings in Banach Space

Let X be a Banach space and F a subset of X. In this paper, we introduce a new iterative scheme to approximate fixed point of mean non-expansive mappings. We first prove that proposed iteration process is faster than all of Mann, Ishikawa, Picard, Agarwal, Noor and Thakur processes for contractive mappings. We also show that some weak and strong convergence theorems for mean non-expansive mappings. Using example presented in mean non-expansive mappings in Banach space. We compare the convergence behavior of the new iterative process with other iterative processes. Keywords. Mean non-expansive mappings, Iterative Process, Uniformly Convex Banach Space, Convergence Theorem.

Enhanced mapping of small-molecule binding sites in cells.

Photoaffinity probes are routinely utilized to identify proteins that interact with small molecules. However, despite this common usage, resolving the specific sites of these interactions remains a challenge. Here we developed a chemoproteomic workflow to determine precise protein binding sites of photoaffinity probes in cells. Deconvolution of features unique to probe-modified peptides, such as their tendency to produce chimeric spectra, facilitated the development of predictive models to confidently determine labeled sites. This yielded an expansive map of small-molecule binding sites on endogenous proteins and enabled the integration with multiplexed quantitation, increasing the throughput and dimensionality of experiments. Finally, using structural information, we characterized diverse binding sites across the proteome, providing direct evidence of their tractability to small molecules. Together, our findings reveal new knowledge for the analysis of photoaffinity probes and provide a robust method for high-resolution mapping of reversible small-molecule interactions en masse in native systems.

O nekim rezultatima fiksne tačke za ekspanzivna preslikavanja u S-metričkim prostorima

Introduction/purpose: The aim of this paper is to establish some existence results of a fixed point for a class of expansive mappings defined on a complete S-metric space. Methods: An iteration scheme was used. Results: Some existing results of mappings satisfying contractive conditions are expanded to expansive ones, providing a new condition expressed in one variable under which the existence of a fixed point holds. Conclusions: This work provides new tools to fixed point theory together with their applications.

Bi-asymptotic c-expansivity

In this paper, we define bi-asymptotically c-expansive maps on metric spaces and study its relationship with other variants of expansivity such as bi-asymptotically expansive maps and N-expansive maps. We also provide an example to establish that expansive homeomorphisms need not be bi-asymptotically expansive. Finally, we prove a spectral decomposition theorem for bi-asymptotically c-expansive continuous surjective maps with the shadowing property on compact metric spaces.

Expansive Type Rational Contraction in Metric Space and Common Fixed Point Theorems

The field of expansive mappings in fixed-point theory is one of the most fascinating areas in mathematics. In this theory, contraction is one of the main tools used to prove a fixed point's existence and uniqueness. For all of the analyses, the fixed point theorem proposed by Banach's contraction theory is highly popular and widely used to prove that a solution to the operator equation Tx=x exists and is unique. Through the present article, we utilize rational expressions in metric spaces to deliver unique common stable (fixed) point results in expansive mapping. The main outcomes of numerous relevant innovations in the newest research are built upon them.

Contraction Type Expansive Map on Complex Valued Metric Space with Fixed Points

According to the present paper, the two self mappings that satisfy contraction type conditions of expansive in complete complex valued metric space reveals that these mappings have some common fixed points. Furthermore, the paper provides generalizations and extensions of well-known results from the existing literature which further expands our understanding of this topic. Some illustrative examples are given to help us obtain results.

The everyday political economy of private security

ABSTRACT In this article we map out a new research agenda for studying private security. We do so by bringing together a series of theoretical, methodological, and geographical ‘turns’ in this area of research that, in our view, signpost the way towards a deeper understanding of this market. The first turn is theoretical and concerns the shift from neoclassical economic interpretations of the market for security towards more political economic readings that excavate the various non-economic structures through which this market is constituted. The second turn is methodological and refers to the move from an (over)reliance on formal-legal, census-like data, towards the embrace of thicker qualitative (often ethnographic) data that gives voice to a range of ground-level perspectives in the market for security. The third turn is geographical and relates to how the long-standing focus on the Anglosphere is giving way to a more expansive map of the market for security that incorporates studies from across Africa, Asia, Continental Europe, and South America. We call this research agenda ‘the everyday political economy of private security’.