characterizations and decomposition of strongly wright-convex functions of higher order
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2015
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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.
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| Authors | ;Attila Gilányi;Nelson Merentes;Kazimierz Nikodem;Zsolt Páles |
| Journal | zhonghua yi xue za zhi |
| Year | 2015 |
| DOI |
http://dx.doi.org/10.7494/OpMath.2015.35.1.37
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