<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper we consider Jessen's functional, defined by means of a positive isotonic linear functional, and investigate its properties. Derived results are then applied to weighted generalized power means, which yields extensions of some recent results, known from the literature. In particular, we obtain the whole series of refinements and converses of numerous classical inequalities such as the arithmetic-geometric mean inequality, Young's inequality and Hölder's inequality</p></abstract>

In this paper we consider Jessen's functional, defined by means of a positive isotonic linear functional, and investigate its properties. Derived results are then applied to weighted generalized power means, which yields extensions of some recent results, known from the literature. In particular, we obtain the whole series of refinements and converses of numerous classical inequalities such as the arithmetic-geometric mean inequality, Young's inequality and Hölder's inequality

Jessen's functional, its properties and applications

Faculty of Civil Engineering and Architecture, Matice hrvatske 15, 21 000 Split, Croatia

Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia

Faculty of Electrical Engineering and Computing, Unska 3, 10000 Zagreb, Croatia

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

{"article-title":"Jessen's functional, its properties and applications"}

In this paper we consider Jessen's functional, defined by means of a positive isotonic linear functional, and investigate its properties. Derived results are...

Jessen's functional, its properties and applications

Published Online: May 17, 2013

Page range: 225 - 248

DOI: https://doi.org/10.2478/v10309-012-0015-6

Keywords
Inequalities, convex function, Jensen's inequality, Jessen's inequality, isotonic functional, Jessen's functional, superadditivity, subadditivity, monotonicity, arithmeticgeometric mean inequality, Young's inequality, Hölder's inequality

This content is open access.

Jessen's functional, its properties and applications

Published Online: May 17, 2013

Page range: 225 - 248

DOI: https://doi.org/10.2478/v10309-012-0015-6

KeywordsInequalities, convex function, Jensen's inequality, Jessen's inequality, isotonic functional, Jessen's functional, superadditivity, subadditivity, monotonicity, arithmeticgeometric mean inequality, Young's inequality, Hölder's inequality

This content is open access.

Keywords
Inequalities, convex function, Jensen's inequality, Jessen's inequality, isotonic functional, Jessen's functional, superadditivity, subadditivity, monotonicity, arithmeticgeometric mean inequality, Young's inequality, Hölder's inequality