TY  - JOUR
ID  - Gilányi2015
LB  - Gilányi2015
AU  - Gilányi, Attila
AU  - Merentes, Nelson
AU  - Nikodem, Kazimierz
AU  - Páles, Zsolt
TI  - Characterizations and decomposition of strongly Wright-convex functions of higher order
ST  - Characterizations and decomposition of strongly Wright-convex functions of higher order
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2015
VL  - 35
IS  - 1
SP  - 37
EP  - 46
DO  - http://dx.doi.org/10.7494/OpMath.2015.35.1.37
UR  - http://dx.doi.org/10.7494/OpMath.2015.35.1.37
AB  - 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.
KW  - generalized convex function
KW  - Wright-convex function of higher order
KW  - strongly convex function
SN  - 1232-9274
ER  -