Viscosity approximation methods with weak contraction for L-Lipschitzian pseudocontractive self-mapping

In this paper, under the framework of real reflexive Banach space which admits a weakly sequentially continuous duality mapping from EE to E∗E∗, we study the strong convergence of an implicit and an explicit composite viscosity approximation algorithm (I) and (II), respectively for a pseudocontractive mapping TT by using the weakly contractive mapping ff as follows: equation(I)xt,s=tf(xt,s)+(1−t)yt,sxt,s=tf(xt,s)+(1−t)yt,syt,s=sxt,s+(1−s)Txt,syt,s=sxt,s+(1−s)Txt,s and equation(II)xn+1=αnf(xn)+(1−αn)yn,xn+1=αnf(xn)+(1−αn)yn,yn=βnxn+(1−βn)Txn,n≥0. Our results unify, improve and complement several recent ones existing in the current literature.