and Applied Analysis 3 Since weak convergence is not good for an effective algorithm, our purpose in this paper is to modify algorithm 1.3 in such a way that strong convergence is guaranteed. More precisely, for any two maximal monotone operators A and B, we define an iterative process in the following way: For x0, u ∈ H given, a sequence xn is generated using the rule x2n 1 αnu δnx2n γnJ βnx2n...

In this paper, we deal with the problem of finding a common fixed point of a family of relatively nonexpansive mappings. We, first of all, discuss the properties of strongly relatively nonexpansive mappings and show a strong convergence theorem for a sequence of relatively nonexpansive mappings under some conditions. Using this result, we obtain a strong convergence theorem for a finite family ...

It is shown that the set of fixed points of a nonexpansive operator is either empty or closed and convex. Under rather general conditions this shows that the minimum norm solution of an operator equation of the form x = Tx exists and is unique, provided that T is nonexpansive. This holds in any strictly convex Banach space, a class of spaces that includes Hilbert spaces as particular case, and ...

and Applied Analysis 3 where A n = α n I + A for all n ≥ 0. In particular, if V ≡ 0, then (11) reduces to the following iterative scheme: x 0 = x ∈ C chosen arbitrarily, y n = P C (x n − ] n A n x n ) , z n = β n x n + γ n P C (x n − ] n A n y n ) + σ n TP C (x n − ] n A n y n ) , x n+1 = P C [λ n (1 − δ n ) γSx n + (I − λ n μF) z n ] , ∀n ≥ 0. (12) Further, if S = V, then (11) reduces to the f...

We prove strong convergence theorems for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a hemirelatively nonexpansive mapping in a Banach space by using monotone hybrid iteration method. By using these results, we obtain new convergence results for resolvents of maximal monotone operators and hemirelatively nonexpansive mappings in a Ban...

Ab8tmctWe examine the representation of signals by the Wavelet 'lhansform Modulus Maxima together with the alternating projection reconstruction algorithm proposed by Mallat. We show that the projection algorithm of Mallat is not minimum distance and not necessarily nonexpansive. Convergence is therefore not guaranteed. We describe an alternative projection operator which is minimum distance an...

Smooth convex optimization problems are solved over fixed point sets of quasi-nonexpansive mappings by using a distributed optimization technique. This is done for a networked system with an operator, who manages the system, and a finite number of users, by solving the problem of minimizing the sum of the operator’s and users’ differentiable, convex objective functions over the intersection of ...