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In this paper, under the framework of real reflexive Banach space which admits a weakly sequentially continuous duality mapping from E to E∗, we study the strong convergence of an implicit and an explicit composite viscosity approximation algorithm (I) and (II), respectively for a pseudocontractive mapping T by using the weakly contractive mapping f as follows: (I)xt,s=tf(xt,s)+(1−t)yt,syt,s=sxt,s+(1−s)Txt,s...
Let H be a Hilbert space and f a fixed contractive mapping with coefficient 0<α<1, A a strongly positive linear bounded operator with coefficient γ̄>0. Consider two iterative methods that generate the sequences {xn},{yn} by the algorithm, respectively. (I)xn=(I−αnA)1tn∫0tnT(s)xnds+αnγf(xn)(II)yn+1=(I−αnA)1tn∫0tnT(s)ynds+αnγf(yn) where {αn} and {tn} are two sequences satisfying certain conditions,...
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