Ishikawa iterates for a pair of maps (Q1074848)

The authors consider an extension of an iteration scheme by Ishikawa to a pair of maps \(T_ 1,T_ 2:C\to C\) on a convex subset C of a normed linear space. With \(\alpha_ n,\beta_ n\in (0,1)\), the process has the form \[ (1)\quad x_ 0\in C,y_ n=\beta_ nT_ 1x_ 1+(1-\beta_ n)x_ n,\quad x_{n+1}=(1-\alpha_ n)x_ n+\alpha_ nT_ 2y_ n, \] \(n=0,1,... \). Under certain generalized contraction conditions convergence results are obtained which extend some results of \textit{S. A. Naimpally} and \textit{K. L. Singh} [J. Math. Anal. Appl. 96, 437-446 (1983; Zbl 0524.47033)]. No applications appear to have provided a motivation for the relatively artificial assumptions. The authors also note that they became aware late of the related work by \textit{G. Das} and \textit{J. P. Debata} [Indian J. Pure. Appl. Math. 15, 713-718 (1984; Zbl 0581.47042)].