On Bregman Best Proximity Points in Banach Spaces

ABSTRACT

In this article, using Bregman functions and Bregman distances, we first introduce the notion of Bregman best proximity points, extending the notion of best proximity points introduced and studied in [1]. We then prove existence and convergence results of Bregman best proximity points for Bregman cyclic contraction mappings in the setting of Banach spaces. It is well known that the Bregman distance does not satisfy either the symmetry property or the triangle inequality which are required for standard distances. Numerical examples are included at the end of the paper. So, our results improve and generalize many known results in the current literature.

KEYWORDS:

• Bregman best proximity point
• Bregman cyclic contraction mapping
• Bregman distance
• Bregman function
• Bregman sharp proximal pair

MATHEMATICS SUBJECT CLASSIFICATION:

• 47H10
• 37C25

Acknowledgements

The author would like to thank the referees for their sincere evaluation and constructive comments which improved the paper considerably.