On a Generalization of Tripled Fixed or Best Proximity Points for a Class of Cyclic Contractive Maps

Abstract

We enrich the known results about tripled fixed points and tripled best proximity points.
We generalize the notion of ordered pairs of cyclic contraction maps and we obtain sufficient conditions for the existence and uniqueness of
fixed (or best proximity) points.
We get a priori and a posteriori error estimates for the tripled fixed points and for the tripled best proximity points, provided that the underlying Banach space has modulus of convexity of power type in the case of best proximity points, obtained by sequences of successive iterations.
We illustrate the main result with an example.