
Journal of Convex Analysis 28 (2021), No. 4, [final page numbers not yet available] Copyright Heldermann Verlag 2021 On kStrong Convexity in Banach Spaces M. Veena Sangeetha Dept. of Mathematics, Indian Institute of Technology, Kharagpur, India veena176@gmail.com M. Radhakrishnan Ramanujan Inst. for Advanced Study in Mathematics, University of Madras, India and: Dept. of Mathematics, SRM University, Andra Pradesh, India radhariasm@gmail.com Samir Kar Dept. of Mathematics, Indian Institute of Technology, Madras, India and: Dept. of Mathematics, Indian Institute of Technology, Jammu, India msamirkar@gmail.com We introduce and study the notion of kstrong convexity in Banach spaces. It is a generalization of the notion of strong convexity first studied by Fan and Glicksberg. A Banach space is said to be kstrongly convex if it is reflexive, kstrictly convex and has the KadecKlee property. We use the idea of kdimensional diameter to give several characterizations of kstrong convexity. Further, we study kstrict convexity and kstrong convexity in some products of Banach spaces. Finally, we give characterizations of kuniform convexity that distinguish it from kstrong convexity. Keywords: kstrict convexity, kstrong convexity, kuniform convexity, property kUC, monotone norm, product space. MSC: 46B20, 41A65. [ Fulltextpdf (161 KB)] for subscribers only. 