By a dynamical system (X, T ) we mean the action of the semigroup (Z,+) on a metrizable topological space X induced by a continuous selfmap T : X → X. Let M(X) denote the set of all compatible metrics on the space X. Our main objective is to show that a selfmap T of a compact space X is a Banach contraction relative to some d1 ∈ M(X) if and only if there exists some d2 ∈ M(X) which, regarded as...

A semi{discrete spatial nite diierence approximation and two fully discrete nite diierence approximations to the complex Ginzburg{Landau equation are considered in this paper. The existence of an inertial manifold is proved inside a discrete H 1 absorbing ball for the semi{discrete approximation by showing certain spectral properties hold for the linear operator and certain Lipschitz properties...

Essential extensions and p-extensions have been studied for commutative rings with identity in various articles, such as [2], [3], and [13]. The present article applies these concepts to certain subrings of C(X). Moreover, the article introduces a new ring extension, called a pg-extension, and determines its relation to both essential extension and p-extension. It turns out that the pg-extensio...

In this paper, we study nonlinear analytic methods for linear contractive operators in Banach spaces. Using these results, we obtain some new strong convergence theorems for commutative families of linear contractive operators in Banach spaces. In the results, the limit points are characterized by sunny generalized nonexpansive retractions.

We examine qualitative properties of solutions of self-consistent Poisson-NernstPlanck (PNP) systems, including uniqueness. In the case of vanishing permanent charge, the predominant case studied, our results unveil a rich structure inherent in these systems, one that is determined by the boundary conditions and the signs of the oppositely charged carrier fluxes. A particularly significant spec...

In this paper, we develop existence and uniqueness criteria to certain class of three point boundary value problems associated with third order nonlinear fuzzy differential equations, with the help of Green’s functions and contraction mapping principle.

1 Local Existence of Evolution Equations 2 1.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 The contraction mapping principle . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Local Existence for Evolution Partial Differential Equations . . . . . . . . . . . . 5 1.4 Local Existence for Nonlinear Heat and Hartree Equations . . . . . . . ...

in this paper, we use the concept of graph convergence of h(.,.)-co-accretive mapping introduced by [r. ahmad, m. akram, m. dilshad, graph convergence for the h(.,.)-co-accretive mapping with an application, bull. malays. math. sci. soc., doi: 10.1007/s40840-014-0103-z, 2014$] and define an over-relaxed proximal point method to obtain the solution of a generalized variational inclusion problem ...

Abstract A thermostat model described by a second-order fractional difference equation is proposed in this paper with one sensor and two sensors boundary conditions depending on positive parameters using the Lipschitz-type inequality. By means of well-known contraction mapping Brouwer fixed-point theorem, we provide new results existence uniqueness solutions. In work use Caputo operator Hyer–Ul...