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Paper IPM / M / 14839  


Abstract:  
We introduce a concept of pointwise cyclic relatively nonexpansive
mapping involving orbits to investigate the existence of best
proximity points using a geometric property defined on a nonempty
and convex pair of subsets of a Banach space X, called weak proximal
normal structure. Examples are given to support our main conclusions.
We also introduce a notion of proximal diametral sequence and establish
a characterization of proximal normal structure and show that every
nonempty and convex pair in uniformly convex in every direction Banach
spaces has weak proximal normal structure. As an application, we give a
new existence theorem for cyclic contractions in reflexive Banach spaces
without strictly convexity condition.
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