Opuscula Math. 35, no. 1 (2015), 37-46

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
  • Received: 2013-09-16.
  • Revised: 2014-03-11.
  • Accepted: 2014-03-21.
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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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