Weak proximal normal structure and coincidence quasi-best proximity points

Farhad Fouladi, Ali Abkar, Erdal Karapinar

Abstract

We introduce the notion of pointwise cyclic-noncyclic relatively nonexpansive pairs involving orbits. We study the best proximity point problem for this class of mappings. We also study the same problem for the class of pointwise noncyclic-noncyclic relatively nonexpansive pairs involving orbits. Finally, under the assumption of weak proximal normal structure, we prove a coincidence quasi-best proximity point theorem for pointwise cyclic-noncyclic relatively nonexpansive pairs involving orbits. Examples are provided to illustrate the observed results.

Keywords

pointwise cyclic-noncyclic pairs; weak proximal normal structure; coincidence quasi-best proximity point

Subject classification

47H09; 46T99; 46B20

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References

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Universitat Politècnica de València

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