begin{abstract} in this paper, we introduce an iterative method for amenable semigroup of non expansive mappings and infinite family of non expansive mappings in the frame work of hilbert spaces. we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. the results present...

in this paper direct proofs of some common fixed point results for two and three mappings under weak contractive conditions are given. some of these results are improved by using different arguments of control functions. examples are presented showing that some generalizations cannot be obtained and also that our results are distinct from the existing ones.

in this paper, a concept of generalized weakly contraction mappings in partially ordered fuzzy metric spaces is introduced and  coincidence point  theorems on partially ordered fuzzy metric spaces are proved. also, as the corollary of these theorems, some common fixed point theorems on partially ordered fuzzy metric spaces are presented.

In this paper, we develop and analyze C0 penalty methods for the fully nonlinear Monge-Ampère equation det(D2u) = f in two dimensions. The key idea in designing our methods is to build discretizations such that the resulting discrete linearizations are symmetric, stable, and consistent with the continuous linearization. We are then able to show the well-posedness of the penalty method as well a...

Abstract. We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat boundary. We observe that, under the nonhomogeneous boundary conditions, the pressure p can be still recovered by solving the Neumann problem for the Po...

in this paper, we study the existence of coupled coincidence andcoupled common fixed points for single-valued and fuzzy mappingsunder a contractive condition in metric space. presented theoremsextend and improve the main results of abbas and$acute{c}$iri$acute{c}$ {itshape et al.} [m. abbas, l.$acute{c}$iri$acute{c}$, {itshape et al.}, coupled coincidenceand common fixed point theorems for hybr...

In this article we investigate the existence of a solution to a semi-linear, elliptic, partial differential equation with distributional coefficients and data. The problem we consider is a generalization of the Lichnerowicz equation that one encounters in studying the constraint equations in general relativity. Our method for solving this problem consists of solving a net of regularized, semi-l...

The Horn-Schunck equations are a coupled system of two partial differential equations which aim at finding motion information in a given image sequence. Recent results [1, 2] asserted that this system is well-posed and can not be decoupled under any linear transformations. In this paper, two alternating iterative algorithms are proposed to solve this system. These algorithms have three properti...

A common method in solving ill-posed problems is to substitute the original problem by a family of well-posed i.e., with a unique solution regularized problems. We will use this idea to define and study a two-step algorithm to solve hierarchical fixed point problems under different conditions on involved parameters. We will see that choosing appropriate hypotheses on the parameters, we will obt...

This thesis is devoted to the study of stochastic nonlinear Schrödinger equations (abbreviated as SNLS) with linear multiplicative noise in two aspects: the wellposedness in L(R), H(R) and the noise effects on blowup phenomena in the non-conservative case. 1. The well-posedness in L(R). The first fundamental question when dealing with SNLS is the well-posedness problem. In the first chapter, we...