### 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)+cx^{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.

Original language | English |
---|---|

Pages (from-to) | 37-46 |

Number of pages | 10 |

Journal | Opuscula Mathematica |

Volume | 35 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2015 |

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### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Opuscula Mathematica*,

*35*(1), 37-46. https://doi.org/10.7494/OpMath.2015.35.1.37

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

Research output: Contribution to journal › Article

*Opuscula Mathematica*, vol. 35, no. 1, pp. 37-46. https://doi.org/10.7494/OpMath.2015.35.1.37

}

TY - JOUR

T1 - Characterizations and decomposition of strongly Wright-convex functions of higher order

AU - Gilányi, Attila

AU - Merentes, Nelson

AU - Nikodem, Kazimierz

AU - Páles, Z.

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

KW - generalized convex function

KW - strongly convex function

KW - Wright-convex function of higher order

UR - http://www.scopus.com/inward/record.url?scp=84911894059&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84911894059&partnerID=8YFLogxK

U2 - 10.7494/OpMath.2015.35.1.37

DO - 10.7494/OpMath.2015.35.1.37

M3 - Article

AN - SCOPUS:84911894059

VL - 35

SP - 37

EP - 46

JO - Opuscula Mathematica

JF - Opuscula Mathematica

SN - 1232-9274

IS - 1

ER -