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

Attila Gilányi, Nelson Merentes, Kazimierz Nikodem, Z. Páles

Research output: Contribution to journalArticle

1 Citation (Scopus)

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)+cxn+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.

Original languageEnglish
Pages (from-to)37-46
Number of pages10
JournalOpuscula Mathematica
Volume35
Issue number1
DOIs
Publication statusPublished - 2015

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Wright Function
Convex function
Higher Order
Decompose
Decomposition Theorem
Generalized Derivatives
Characterization Theorem
Polynomial function
If and only if

Keywords

  • generalized convex function
  • strongly convex function
  • Wright-convex function of higher order

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Characterizations and decomposition of strongly Wright-convex functions of higher order. / Gilányi, Attila; Merentes, Nelson; Nikodem, Kazimierz; Páles, Z.

In: Opuscula Mathematica, Vol. 35, No. 1, 2015, p. 37-46.

Research output: Contribution to journalArticle

Gilányi, Attila ; Merentes, Nelson ; Nikodem, Kazimierz ; Páles, Z. / Characterizations and decomposition of strongly Wright-convex functions of higher order. In: Opuscula Mathematica. 2015 ; Vol. 35, No. 1. pp. 37-46.
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