Refinement of inequalities related to convexity via superquadracity, weaksuperquadracity and superterzacity

Shoshana Abramovich; Slavica Ivelić; Josip Pečarić

doi:10.1007/978-3-0348-0249-9_15

Refinement of inequalities related to convexity via superquadracity, weaksuperquadracity and superterzacity

Shoshana Abramovich, Slavica Ivelić, Josip Pečarić

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

This paper is about inequalities satisfied by functions called superterzatic and their relations to convex and to superquadratic functions. In analogy to inequalities satisfied by convex and by superquadratic functions that are reduced to equalities when f(x)=x, f(x)=x², x≥0 respectively, the inequalities satisfied by superterzatic functions reduce to equalities when f(x)=x³, x≥0. In particular, we deal here with the generalization of the inequality x,y≥0, q≥3, that reduces to equality for q=3.

Original language	English
Title of host publication	International Series of Numerical Mathematics
Publisher	Springer
Pages	191-207
Number of pages	17
DOIs	https://doi.org/10.1007/978-3-0348-0249-9_15
State	Published - 2012

Publication series

Name	International Series of Numerical Mathematics
Volume	161
ISSN (Print)	0373-3149
ISSN (Electronic)	2296-6072

Bibliographical note

Publisher Copyright:
© 2012, Springer Basel.

Keywords

Convexity
Jensen inequality
Jensen-Steffensen inequality
Superquadracity
Superterzacity
Weaksuperquadracity
Weaksuperterzacity

ASJC Scopus subject areas

Numerical Analysis
Control and Optimization
Applied Mathematics

Access to Document

10.1007/978-3-0348-0249-9_15

Cite this

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abstract = "This paper is about inequalities satisfied by functions called superterzatic and their relations to convex and to superquadratic functions. In analogy to inequalities satisfied by convex and by superquadratic functions that are reduced to equalities when f(x)=x, f(x)=x2, x≥0 respectively, the inequalities satisfied by superterzatic functions reduce to equalities when f(x)=x3, x≥0. In particular, we deal here with the generalization of the inequality x,y≥0, q≥3, that reduces to equality for q=3.",

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Refinement of inequalities related to convexity via superquadracity, weaksuperquadracity and superterzacity. / Abramovich, Shoshana; Ivelić, Slavica; Pečarić, Josip.
International Series of Numerical Mathematics. Springer, 2012. p. 191-207 (International Series of Numerical Mathematics; Vol. 161).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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AU - Pečarić, Josip

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KW - Convexity

KW - Jensen inequality

KW - Jensen-Steffensen inequality

KW - Superquadracity

KW - Superterzacity

KW - Weaksuperquadracity

KW - Weaksuperterzacity

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BT - International Series of Numerical Mathematics

PB - Springer

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Refinement of inequalities related to convexity via superquadracity, weaksuperquadracity and superterzacity

Abstract

Publication series

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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