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Shunmugaraj, P.; Zalinescu, Constantin

Compactly locally uniformly convex functions. (English) Zbl 07928055

J. Convex Anal. 31, No. 4, 1245-1272 (2024).
Summary: We introduce compactly locally uniformly convex functions and present their properties, as well as their relations with other classes of convex functions.

MSC:

26B25 Convexity of real functions of several variables, generalizations
46G05 Derivatives of functions in infinite-dimensional spaces
49N15 Duality theory (optimization)
58C20 Differentiation theory (Gateaux, Fréchet, etc.) on manifolds
46B20 Geometry and structure of normed linear spaces
54C50 Topology of special sets defined by functions

Keywords:

locally uniformly convex function; compactly locally uniformly convex function; nearly strongly convex function; locally nearly uniformly convex function; locally nearly uniformly smooth function
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References:

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