Opuscula Math. 35, no. 1 (2015), 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

Attila Gilányi
Nelson Merentes
Kazimierz Nikodem
Zsolt Páles

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.

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• Attila Gilányi
• University of Debrecen, Faculty of Informatics, Pf. 12, 4010 Debrecen, Hungary
• Nelson Merentes
• Universidad Central de Venezuela, Escuela de Matemáticas, Caracas, Venezuela
• Kazimierz Nikodem
• University of Bielsko-Biała, Department of Mathematics and Computer Science, ul. Willowa 2, 43-309 Bielsko-Biała, Poland
• Zsolt Páles
• University of Debrecen, Institute of Mathematics, Pf. 12, 4010 Debrecen, Hungary
• Revised: 2014-03-11.
• Accepted: 2014-03-21.

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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