@Article{Gilányi2015,
author = "Gilányi, Attila and Merentes, Nelson and Nikodem, Kazimierz and Páles, Zsolt",
title = "Characterizations and decomposition of strongly Wright-convex functions of higher order",
journal = "Opuscula Math.",
year = "2015",
volume = "35",
number = "1",
pages = "37--46",
doi = "http://dx.doi.org/10.7494/OpMath.2015.35.1.37",
url = "http://dx.doi.org/10.7494/OpMath.2015.35.1.37",
abstract = "Motivated by results on strongly convex and strongly Jensen-convex functions by R. Ger and K. Nikodem in [Strongly convex functions of higher order, Nonlinear Anal. 74 (2011), 661-665] we investigate strongly Wright-convex functions of higher order and we prove decomposition and characterization theorems for them. Our decomposition theorem states that a function \(f\) is strongly Wright-convex of order \(n\) if and only if it is of the form \(f(x)=g(x)+p(x)+c x^{n+1}\), where \(g\) is a (continuous) \(n\)-convex function and \(p\) is a polynomial function of degree \(n\). This is a counterpart of Ng's decomposition theorem for Wright-convex functions. We also characterize higher order strongly Wright-convex functions via generalized derivatives.",
keywords = "generalized convex function, Wright-convex function of higher order, strongly convex function",
issn = "1232-9274"
}