A Common Fixed Point Theorem Using an Iterative Method

Let H be a Hilbert space and C be a closed, convex and nonempty subset of H. Let T : C → H be a non-self and non-expansive mapping. V. Colao and G. Marino with particu lar choice of the sequence {αn} in Krasonselskii-Mann algorithm, xn+1 = αnxn + (1 − αn)T(xn), proved both weak and strong con verging results. In this paper, we generalize their algorithm and result, imposing some conditions upon the set C and finite many mappings from C in to H, to obtain a converging sequence to a common fixed point for these non-self and non-expansive mappings.