Opuscula Mathematica
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.
Cite this article as:
Attila Gilányi, Nelson Merentes, Kazimierz Nikodem, Zsolt Páles, Characterizations and decomposition of strongly Wright-convex functions of higher order, Opuscula Math. 35, no. 1 (2015), 37-46, http://dx.doi.org/10.7494/OpMath.2015.35.1.37
 
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ISSN 1232−9274, e-ISSN 2300−6919, DOI http://dx.doi.org/10.7494/OpMath
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