Abstract In this work we introduce and analyse a new multiscale method for strongly nonlinear monotone equations in the spirit of localized orthogonal decomposition. A problem-adapted space is constructed by solving linear local fine-scale problems, which then used generalized finite element method. The linearity problems allows their localization and, moreover, makes very efficient to use. giv...

We introduce an iterative sequence for finding a common element of the set of fixed points of a nonexpansive mapping and the solutions of the variational inequality problem for three inversestrongly monotone mappings. Under suitable conditions, some strong convergence theorems for approximating a common element of the above two sets are obtained. Moreover, using the above theorem, we also apply...

The purpose of this paper is to find of the theoretical results of fixed point theorems for a mixed monotone mapping in a metric space endowed with partially order by using the generalized Kanann type contractivity of assumption. Also, as an application, we prove the existence and uniqueness of solution for a first-order ordinary differential equation with periodic bou...

In this paper, we introduce a viscosity iterative process, which converges strongly to a common element of the set of fixed points of a pseudo-contractive mapping and the set of solutions of a monotone mapping. We also prove that the common element is the unique solution of certain variational inequality. The strong convergence theorems are obtained under some mild conditions. The results prese...

We introduce a new iterative method for finding a common element of the set of solutions of a generalized equilibrium problem with a relaxed monotone mapping and the set of common fixed points of a countable family of nonexpansive mappings in a Hilbert space and then prove that the sequence converges strongly to a common element of the two sets. Using this result, we prove several new strong co...

We study stability properties of a proximal point algorithm for solving the inclusion 0 ∈ T (x) when T is a set-valued mapping that is not necessarily monotone. More precisely we show that the convergence of our algorithm is uniform, in the sense that it is stable under small perturbations whenever the set-valued mapping T is metrically regular at a given solution. We present also an inexact pr...

Consider the variational inequality V I(C, F ) of finding a point x∗ ∈ C satisfying the property 〈Fx∗, x − x∗〉 ≥ 0 for all x ∈ C, where C is a nonempty closed convex subset of a real Hilbert space H and F : C → H is a nonlinear mapping. If F is boundedly Lipschitzian and strongly monotone, then we prove that V I(C, F ) has a unique solution and iterative algorithms can be devised to approximate...