Search

The point of this paper is to present and study the idea of higher derivations on partially ordered sets that generalize the concept of derivations on partially ordered sets. Additionally, several characterization theorems on higher derivations are introduced. Moreover, the properties of the fixed points based on the higher derivations are examined. Finally, the properties of ideals and operations related to higher derivations are studied. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a modified Mann iterative scheme for solving a split equality proximal point algorithm problem. We also establish strong convergence of this iterative sequence to a minimizer of a convex function which is also a common fixed point of a nonspreading-type multi-valued mapping in Hilbert space. [ABSTRACT FROM AUTHOR]

In this paper, we use Krasnoselskii's fixed point theorem to study the existence and uniqueness of periodic solutions of a class of iterative differential equation... where K 2 R \ {0},ai 2 R, fi(t) denotes ith iterate of f (t), i = 1,2, . . ., n. The above equation is closely related to a discrete derivatives sequence F0(m) (see [Y.-F.S. P'etermann, Jean-Luc R'emy, Ilan Vardi, Discrete derivatives of sequences, Adv. in Appl. Math. 27 (2001) 562-584]). [ABSTRACT FROM AUTHOR]

In this paper, we consider an iterative procedure for approximating common fixed points of two generalized asymptotically quasi-nonexpansive mappings and we prove some strong and weak convergence theorems for such mappings in uniformly convex Banach spaces.This will extend the results of Cholamjiak and Suantai, Khan and those generalized therein to the case of generalized asymptotically quasi-nonexpansive mappings and by a faster iterative procedure. [ABSTRACT FROM AUTHOR]

In this paper, we prove some common fixed point theorems for the mappings satisfying Prešić type contractive conditions in metric spaces. Our results generalize and extend the result of Prešić for some new type of contractive conditions. The common fixed point of mappings is approximated by a k-step iterative sequence. Some examples are provided to illustrate the results. An application of Prešić type mappings to second order difference equations is also given. [ABSTRACT FROM AUTHOR]

This work presents a quasi-static model for adhesive contact between an elastic membrane with damage and a rigid obstacle that lies beneath it. The model consists of an elliptic variational inequality for the membrane displacements, a nonlinear ordinary differential equation for the evolution of the adhesion field and a parabolic variational inequality for the damage field. By using regularity results from the theory of elliptic variational inequalities and a fixed point argument, the system is shown to have a unique weak solution. [ABSTRACT FROM AUTHOR]

We study a mechanical problem modeling the antiplane shear deformation of a cylinder in frictional contact with a rigid foundation. The material is assumed to be thermo-viscoelastic with long-term memory, the process is quasistatic, and the friction is modeled with Tresca's law. The mechanical model is described as a coupled system of a variational elliptic equality for the displacements and a differential heat equation for the temperature. We present a variational formulation of the problem and establish the existence and uniqueness of weak solution in using general results on evolution equations with monotone operators and fixed point arguments. [ABSTRACT FROM AUTHOR]

Let us consider a non-self mapping T : A ℯ B, where A and B are two nonempty subsets of a partially ordered set that is equipped a metric. A best proximity point x * for such a mapping T is a point such that d(x*, Tx*) = dist(A,B). In this work, we provide different existence results of best proximity points and so, we establish some new fixed point theorems in the setting of partially ordered set. [ABSTRACT FROM AUTHOR]

We consider an abstract nonlinear multi-valued reaction-diffusion system with delay and, using some compactness arguments coupled with metric fixed point techniques, we prove some sufficient conditions for the existence of at least one C0-solution. [ABSTRACT FROM AUTHOR]