DOI: 10.24193/fpt-ro.2021.1.29

Authors: Boyan Zlatanov

Abstract: We enrich the known results about coupled fixed points and coupled 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 best proximity points. We get a priori and a posteriori error estimates for the coupled fixed points and for the coupled 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.

Key Words and Phrases: Coupled best proximity points, uniformly convex Banach space, modulus of convexity, a priori error estimate, a posteriori error estimate, system of linear equations.

2010 Mathematics Subject Classification: 41A25, 47H10, 54H25, 46B20, 47H10.

Published on-line: February 1st, 2021.

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