Journal of Convex Analysis 31 (2024), No. 4, 1245--1272
Copyright Heldermann Verlag 2024
Compactly Locally Uniformly Convex Functions
Palanikumar Shunmugaraj
Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, India
psraj@iitk.ac.in
Constantin Zalinescu
(1) Octav Mayer Institute of Mathematics, Iasi, Romania
(2) Faculty of Mathematics, University "Al. I. Cuza", Iasi, Romania
zalinesc@uaic.ro
We introduce compactly locally uniformly convex functions and present their properties, as well as their relations with other classes of convex 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.
MSC: 26B25, 46G05, 49N15, 58C20; 46B20, 54C50.
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