GENERALIZED CONVEXITY AND PASSAGE FROM LOCAL TO GLOBAL VIA DIFFERENTIAL INEQUALITIES

Kocak S., Limoncu M.

REAL ANALYSIS EXCHANGE, cilt.47, sa.1, ss.103-120, 2022 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 47 Sayı: 1
  • Basım Tarihi: 2022
  • Doi Numarası: 10.14321/realanalexch.47.1.1602263520
  • Dergi Adı: REAL ANALYSIS EXCHANGE
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, MathSciNet, Public Affairs Index, zbMATH, DIALNET
  • Sayfa Sayıları: ss.103-120
  • Anahtar Kelimeler: generalized convexity, differential inequality, Alexandrov geometry
  • Anadolu Üniversitesi Adresli: Evet

Özet

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.