Abstract
In this paper we use a matrix approach to approximate solutions of variational inequalities in Hilbert spaces. The methods studied combine new or well-known iterative methods (as the original Mann method) with regularized processes that involve regular matrices in the sense of Toeplitz. We obtain ergodic type results and convergence.
Highlights
Introduction and resultsThe results presented here will be proved in Section .Let H be a Hilbert space and let f : H → H be a ρ-contraction
In this paper our aim is to approximate on Fix(T) the unique solution of a (VIP) when T is a nonspreading mapping, i.e
In Mann [ ], taking in account the works of Cesaro, Fejer and Toeplitz, considered the problem to construct a sequence in a convex and compact set C of a Banach space X that converges to a fixed point of a continuous transformation T : C → C
Summary
Introduction and resultsThe results presented here will be proved in Section .Let H be a Hilbert space and let f : H → H be a ρ-contraction. It is well known that if T : H → H is a quasi-nonexpansive mapping, the set of the fixed points Fix(T) is closed and convex and the variational inequality problem (VIP) The weak limits of a regularized sequence that involves a nonspreading mapping and a triangular-Toeplitz matrix are fixed points of T; more precisely, we will prove the following.
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