GENERALIZED CONVEXITY AND PASSAGE FROM LOCAL TO GLOBAL VIA DIFFERENTIAL INEQUALITIES

Kocak S., Limoncu M.

REAL ANALYSIS EXCHANGE, vol.47, no.1, pp.103-120, 2022 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.14321/realanalexch.47.1.1602263520
  • Journal Name: REAL ANALYSIS EXCHANGE
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, MathSciNet, Public Affairs Index, zbMATH, DIALNET
  • Page Numbers: pp.103-120
  • Keywords: generalized convexity, differential inequality, Alexandrov geometry
  • Anadolu University Affiliated: Yes

Abstract

We give an elementary framework of generalized convexity in terms of comparison of a given function with reference functions from a chosen set. As important examples we consider reference sets used in Alexandrov geometry and give simple proofs for the characterization of generalized convexity in form of differential inequalities.