Abstract
Let T and I be two compatible self maps of a closed, convex bounded subset C of a Normed space X such that I(C) superset-or-equal-to (1 - k).I(C)+k.T(C) where 0 < k < 1 is fixed and parallel-to Tx - Ty parallel-to(p) less-than-or-equal-to a . parallel-to Ix - Iy parallel-to(p) + (1 - a) . max [parallel-to Tx - Ix parallel-to(p), parallel-to Ty - Iy parallel-to(p] for all x, y is-an-element-of C, where 0 < a < 1 and p > 0. If for some x0 is-an-element-of C, the sequence [x(n)] defined by Ix(n+1) = (1 - k) . Ix(n) + k . Tx(n), for all n greater-than-or-equal-to 0, converges to a point z in C and if I is continuous at z then T and I have a unique common fixed point. Further if I is continuous at Tz then I have a unique common fixed point at which T is continuous. We have also applied this result to obtain iterative solution of certain variational inequalities.