‎in a real hilbert space‎, ‎an iterative scheme is considered to‎ ‎obtain strong convergence which is an essential tool to find a‎ ‎common fixed point for a countable family of nonexpansive mappings‎ ‎and the solution of a variational inequality problem governed by a‎ ‎monotone mapping‎. ‎in this paper‎, ‎we give a procedure which results‎ ‎in developing shehu's result to solve equilibrium prob...

In this article, we study a nonlinear fourth-order differential equation two-point boundary value problem. We use monotone iterative technique and lower and upper solutions of completely continuous operators to get the existence of nontrivial solutions for the problem. The results can guarantee the existence of nontrivial sign-changing solutions and positive solutions, and we can construct two ...

where t ∈ T = [ν – β – 1,b + ν – β – 1]Nν–β–1 . βν–2, b∇ν are left and right fractional difference operators, respectively, and φp(s) = |s|p–2s, p > 1. By using the method of upper and lower solution and the Schauder fixed point theorem, we obtain the existence of positive solutions for the above boundary value problem; and applying a monotone iterative technique, we establish iterative schemes...

In this paper, by employing the fixed point theory and the monotone iterative technique, we investigate the existence of a unique solution for a class of nonlinear fractional integrodifferential equations on semi-infinite domains in a Banach space. An explicit iterative sequence for approximating the solution of the boundary value problem is derived. An error estimate is also given. © 2013 Else...

A new parallel implementation of quantum confinement effects simulations for semiconductor devices is presented. In this simulation, a set of self-consistent Schrödinger and Poisson (SP) equations is solved with parallel divide and conquer and monotone iterative algorithms on a Linux-cluster with message-passing interface (MPI) library. To solve the Schrödinger equation, instead of the conventi...