Convergence of Ishikawa’s iteration method for pseudocontractive mappings

Let CC be a nonempty, closed and convex subset of a real Hilbert space HH. Let Ti:C→C,i=1,2,…,NTi:C→C,i=1,2,…,N, be a finite family of Lipschitz pseudocontractive mappings. It is our purpose, in this paper, to prove strong convergence of Ishikawa’s method to a common fixed point of a finite family of Lipschitz pseudocontractive mappings provided that the interior of the common fixed points is nonempty. No compactness assumption is imposed either on TT or on CC. Moreover, computation of the closed convex set CnCn for each n≥1n≥1 is not required. The results obtained in this paper improve on most of the results that have been proved for this class of nonlinear mappings.