Characterizations of higher-order convexity properties with respect to Chebyshev systems
Using the general Chebyshev systems \(\omega \) the authors introduce various notions of convexity of real functions (\(\omega \) -convexity, \(\left( t,\omega \right) \)-convexity, \(\omega \)-Jensen convexity) and extend some standard convexity results presented in [\textit{A. Gilańyi} and \textit{Z. Páles}, Math. Inequal. Appl. 11, No. 2, 271--282 (2008; Zbl 1141.26304)] and [\textit{K. Nikodem} and \textit{Z. Páles}, Real Anal. Exch. 29, No. 1, 219--228 (2004; Zbl 1076.26008)]. They obtain various characterizations of convexity properties in terms of the nonnegativity of a generalized divided difference and the corresponding lower Dinghas type derivative. Among others, they show that these convexity properties are localizable.
generalized lower Dinghas type derivative
scientific article; zbMATH DE number 6563693