Characterizations of inner product spaces by strongly convex functions

Kazimierz Nikodem, Z. Páles

Research output: Contribution to journalArticle

41 Citations (Scopus)

Abstract

New characterizations of inner product spaces among normed spaces involving the notion of strong convexity are given. In particular, it is shown that the following conditions are equivalent: (1) (X, || · ||) is an inner product space; (2) f : X → ℝ is strongly convex with modulus c > 0 if and only if f - c|| · ||2 is convex; (3) || · ||2 is strongly convex with modulus 1.

Original languageEnglish
Pages (from-to)83-87
Number of pages5
JournalBanach Journal of Mathematical Analysis
Volume5
Issue number1
Publication statusPublished - 2011

Fingerprint

Inner product space
Convex function
Modulus
Normed Space
Convexity
If and only if

Keywords

  • Inner product space
  • Strongly convex function
  • Strongly midconvex function

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis

Cite this

Characterizations of inner product spaces by strongly convex functions. / Nikodem, Kazimierz; Páles, Z.

In: Banach Journal of Mathematical Analysis, Vol. 5, No. 1, 2011, p. 83-87.

Research output: Contribution to journalArticle

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