In this paper, we consider double sequence iteration processes for strongly $rho$-contractive mapping in modular space. It is proved, these sequences, convergence strongly to a fixed point of the strongly $rho$-contractive mapping.

Zero point problems of the sum of two monotone mappings and fixed point problems of a strictly pseudocontractive mapping are investigated‎. ‎A strong convergence theorem for the common solutions of the problems is established in the framework of Hilbert spaces‎.

In real Hilbert spaceH , from an arbitrary initial point x0 ∈H , an explicit iteration scheme is defined as follows: xn+1 = αnxn + (1 − αn)Tn+1xn,n ≥ 0, where Tn+1xn = Txn − λn+1μF(Txn), T :H →H is a nonexpansive mapping such that F(T) = {x ∈ K : Tx = x} is nonempty, F :H →H is a η-strongly monotone and k-Lipschitzian mapping, {αn} ⊂ (0,1), and {λn} ⊂ [0,1). Under some suitable conditions, the ...

We consider a generalized equation governed by strongly monotone and Lipschitz single-valued mapping maximally set-valued in Hilbert space. are interested the sensitivity of solutions w.r.t. perturbations both mappings. demonstrate that directional differentiability solution map can be verified using operator resolvent mapping. The result is applied to quasi-generalized equations which we have ...

Let E be a 2-uniformly convex real Banach space with uniformly Gâteaux differentiable norm, and [Formula: see text] its dual space. Let [Formula: see text] be a bounded strongly monotone mapping such that [Formula: see text] For given [Formula: see text] let [Formula: see text] be generated by the algorithm: [Formula: see text]where J is the normalized duality mapping from E into [Formula: see ...

We study distributed algorithms for seeking a Nash equilibrium in class of convex networked games with strongly monotone mappings. Each player has access to her own smooth local cost function and can communicate neighbors some undirected graph. To deal fast learning equilibria under such settings, we introduce so called augmented game mapping provide conditions which this is monotone. consider ...

In this paper, a new three-step iterative scheme is introduced for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality for α-inverse-strongly monotone mappings. The result reveals that the proposed iterative sequence converges strongly to the common element of this two. And our studies can be regarded as an extensi...

A new approximationmethod for solving variational inequalities and fixed points of nonexpansive mappings is introduced and studied. We prove strong convergence theorem of the new iterative scheme to a common element of the set of fixed points of nonexpansive mapping and the set of solutions of the variational inequality for the inverse-strongly monotone mapping which solves some variational ine...

Symmetries play an important role in the dynamics of physical systems. As example, quantum physics and microworld are basis symmetry principles. These problems reduced to solving inequalities general. That is why this article, we study numerical approximation solutions variational inequality involving quasimonotone operators infinite-dimensional real Hilbert space. We prove that iterative seque...