Viscosity Approximation of a Zero of Accretive Operator in Banach Space 1
Yanrong Yu, Yujun Liu, Rudong Chen · 2007
Abstract. This paper introduces a iteration scheme for viscosity approxi-mation of a zero of accretive operator in a reflexive Banach space with weakly continuous duality mapping. This new iteration scheme is defined as follows:⎧⎪⎨ x0 ∈ C chosen arbitrarily yn = αnxn + (1 − αn)Jrnxn, n ≥ 0 xn+1 = βnf(xn) + (1 − βn)yn, n ≥ 0 where f is a contraction and Jr denotes resolvent (I + rA) −1 for r> 0, se-quences {αn}∞n=0 and {βn}∞n=0 in (0, 1). Under certain appropriate assumptions on the sequences {αn} and {βn}, strong convergence of the algorithm {xn} is proved. The results improve and extend the results of T.H.Kim, H.K.Xu and some others.