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 ...

We introduce an iterative scheme for finding a common element of the set of common fixed points of a family of infinitely nonexpansive mappings, and the set of solutions of the variational inequality for an inverse-strongly monotone mapping in a Hilbert space. Under suitable conditions, some strong convergence theorems for approximating a common element of the above two sets are obtained. As ap...

In this paper, we propose an explicit viscosity approximation method for finding a common element of the set of fixed points of strict pseudo-contractions and of the set of solutions of variational inequalities with inverse-strongly monotone mappings. Strong convergence theorems are established in the framework of Hilbert spaces. 2000 Mathematics Subject Classification: 47H05, 47H09, 47J25

and Applied Analysis 3 The generalized mixed equilibrium problems with perturbation is very general in the sense that it includes fixed point problems, optimization problems, variational inequality problems, Nash equilibrium problems, and equilibrium problems as special cases see, e.g., 4, 5 . Numerous problems in physics, optimization, and economics reduce to find a solution of problem 1.2 . S...

The purpose of this paper is to introduce a general iterative process for the problem of finding a common element in the set of common fixed points of an infinite family of nonexpansive mappings and in the set of solutions of variational inequalities for inverse-strongly monotone mappings.

We introduce an iterative method for finding a common element of set of fixed points of nonexpansive mappings, the set of solutions of a finite family of variational inclusion with setvalued maximal monotone mappings and inverse strongly monotone mappings, and the set of solutions of a mixed equilibrium problem in Hilbert spaces. Under suitable conditions, some strong convergence theorems for a...

The purpose of this paper is to introduce a new iterative scheme for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of solutions of variational inequality problems, the zero point of maximal monotone operators, and the set of two countable families of quasi-φ-nonexpansive mappings in Banach spaces. Moreover, the strong convergence theorems of...