On some application on coupled and best proximity points theorems

Abstract

We enrich the known applications of coupled best proximity points theorems for ordered pair (F; G) of cyclic contraction maps. We present a procedure to construct such pairs of cyclic contraction maps that will give the best possible rate of convergence, when solving linear systems. We give numerical computations for the a priori and a posteriori error estimates, obtained by a sequence of successive iterations. We give an upper bound for the best possible rate of convergence if coupled best proximity points theorems are used to solve these linear systems. We illustrate some newly obtained generalizations about coupled best proximity points with a number of example.