A new iteration process for generalized Lipschitz pseudo-contractive and generalized Lipschitz accretive mappings

摘要

Let K be a nonempty closed convex subset of a real Banach space E. Let T:K→K be a generalized Lipschitz pseudo-contractive mapping such that F(T){xK:Tx=x}≠0/. Let and {θn}n≥1 be real sequences in (0,1) such that and λn(αn+θn)<1. From arbitrary x1K, let the sequence {xn}n≥1 be iteratively generated by xn+1=(1-λnan)xn+λnantTxn-λnθn(xn-x1) Then, {xn}n≥1 is bounded. Moreover, if E is a reflexive Banach space with uniformly Gateaux differentiable norm and if ∑_(n=1)~∞ λnθn=∞ is additionally assumed, then, under mild conditions, {xn}n≥1 converges strongly to some x*F∈(T).