An approximation method for strictly pseudocontractive mappings Original Research Article

Let KK be a closed convex subset of a qq-uniformly smooth separable Banach space, T:K→KT:K→K a strictly pseudocontractive mapping, and f:K→Kf:K→K an LL-Lispschitzian strongly pseudocontractive mapping. For any t∈(0,1)t∈(0,1), let xtxt be the unique fixed point of tf+(1-t)Ttf+(1-t)T. We prove that if TT has a fixed point, then {xt}{xt} converges to a fixed point of TT as tt approaches to 0.