Min-max property in metric spaces with convex structure
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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- 12.A. L. Garkavi, On the Chebyshev center of a set in a normed space, in: Investigations of Contemporary Problems in the Constructive Theory of Functions, Fizmatgiz. (Moscow, 1961), pp. 328–331 (in Russian).Google Scholar
- 13.W. A. Kirk, Geodesic geometry and fixed point theory, II, in: Proceedings of the International Conference on Fixed Point Theory and Applications, (Valencia, Spain, July 2003), Yokohama Publ. (Yokohama, 2004), pp. 113–142.Google Scholar