Min-max property in metric spaces with convex structure
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In the setting of convex metric spaces, we introduce the two geometric notions of uniform convexity in every direction as well as sequential convexity. They are used to study a concept of proximal normal structure. We also consider the class of noncyclic relatively nonexpansive mappings and analyze the min-max property for such mappings. As an application of our main results we conclude with some best proximity pair theorems for noncyclic mappings.
Key words and phrasesproximal normal structure noncyclic relatively nonexpansive mapping uniformly in every direction convex metric space
Mathematics Subject Classification54E35 47H09 46B20
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