HYBRID VISCOSITY ITERATIVE APPROXIMATION OF ZEROS OF M-ACCRETIVE OPERATORS IN BANACH SPACES

Abstract

In this paper, let $X$ be a reflexive Banach space which either is uniformly smooth or has a weakly continuous duality map. We prove, under the convergence of no parameter sequences to zero, the strong convergence of their iterative scheme to a zero of $m$-accretive operator $A$ in $X$, which solves a variational inequality on the set $A^{-1}(0)$ of zeros of $A$. Such a result includes their main result as a special case. Furthermore, we also give a weak convergence theorem for hybrid viscosity iterative approximation method involving a maximal monotone operator in a Hilbert space.