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Min-max property in metric spaces with convex structure

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Abstract

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.

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Correspondence to M. Gabeleh.

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The first author was partially supported by a grant from IPM (No. 96470046).

The second author acknowledges partial support from the National Research foundation of South Africa under grant 114773.

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Gabeleh, M., Künzi, HP.A. Min-max property in metric spaces with convex structure. Acta Math. Hungar. 157, 173–190 (2019). https://doi.org/10.1007/s10474-018-0857-0

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  • DOI: https://doi.org/10.1007/s10474-018-0857-0

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