Communications of the
Korean Mathematical Society CKMS

Strong convergence theorems on viscosity approximation me\-thods for finding a common zero of a finite family accretive operators are established in a reflexive and strictly Banach space having a uniformly G\^ateaux differentiable norm. The main theorems supplement the recent corresponding results of Wong et al. \cite{WoSaYa} and Zegeye and Shahzad \cite{ZeSh} to the viscosity method together with different control conditions. Our results also improve the corresponding results of \cite{Ju0,Ki,LiLeLi,MaSa,SeDo} for finite nonexpansive mappings to the case of finite pseudocontractive mappings.

Keywords: strong convergence, variational inequalities, nonexpansive mapping, fixed points, accretive operator, resolvent, sunny and nonexpansive retraction, strictly convex, uniformly G\^ateaux differentiable norm

MSC numbers: 47H06, 47H10, 47J25, 49M05