Communications in Mathematical Analysis

Jensen-Type Inequalities on Time Scales For $n$-Convex Functions

Rozarija Mikic and Josip Pecaric

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Abstract

By utilizing some scalar inequalities obtained via Hermite's interpolating polynomial, we will obtain lower and upper bounds for the difference in Jensen's inequality and in the Edmundson-Lah-Ribaric inequality in time scale calculus that hold for the class of $n$-convex functions. Main results are then applied to generalized means, with a particular emphasis to power means, and in that way some new reverse relations for generalized and power means that correspond to $n$-convex functions are obtained.

Article information

Source
Commun. Math. Anal., Volume 21, Number 2 (2018), 46-67.

Dates
First available in Project Euclid: 21 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.cma/1545361386

Mathematical Reviews number (MathSciNet)
MR3896534

Zentralblatt MATH identifier
07002175

Subjects
Primary: 26D15: Inequalities for sums, series and integrals 26E70: Real analysis on time scales or measure chains {For dynamic equations on time scales or measure chains see 34N05} 26A51: Convexity, generalizations

Keywords
Time scale linear functional Jensen's inequality $n$-convex functions means

Citation

Mikic, Rozarija; Pecaric, Josip. Jensen-Type Inequalities on Time Scales For $n$-Convex Functions. Commun. Math. Anal. 21 (2018), no. 2, 46--67. https://projecteuclid.org/euclid.cma/1545361386


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