Let (X, d) be a complete convex metric space, and C be a nonempty, closed and convex subset of X. We consider Ćirić type contractive self-mappings T of C satisfying: for all x, y ∈ C, where 0 < a < 1, a + b = 1, and c ≥ 0. We give a simple proof to an extension of Ćirić's fixed point theorem [4] and Gregus’ fixed point theorem [9], and present some results on the approximation of fixed points. In particular, we show that the least upper bound of c for T to have a fixed point is , which is therefore independent of a and b.
