Opuscula Math. 35, no. 1 (), 37-46
http://dx.doi.org/10.7494/OpMath.2015.35.1.37
Opuscula Mathematica

# Characterizations and decomposition of strongly Wright-convex functions of higher order

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.
Mathematics Subject Classification: 26A51, 39B62.