Approximation of Fixed Points of Asymptotically k-strict Pseudocontractive Mapping in the Intermediate Sense in Banach Space

Let E be a real Banach space and C be a nonempty closed convex subset of E.T:C→C is a uniformly L-Lipschitz asymptotically k-strict pseudocontractive mapping in the intermediate sense and ∑∞ n=1γn∞.Let x0∈E be any given point,{xn}is the modified Mann iterative sequence with errors defined by xn+1=(1-αn-βn)xn+αnTnxn+βnun.If F(T)is nonempty and bounded,under some appropriate restricted conditions,a necessary and sufficient condition forxnconverges strongly to a fixed point of T islim infn→∞ D{xn},FT=0.After removing the condition that F(T) is bounded,under the same restricted conditions on the parameters,the modified Mann iterative sequencexndefined by {xn}+1=(1-αn)xn+αnTnxn converges strongly to a fixed point of T if and only if lim infn→∞ D(xn,F(T))=0.