This article is cited in 3 papers

On Willett's, Godunova–Levin's, and Rozanova's Opial-Type Inequalities with Related Stolarsky-Type Means

M. Andric^a, A. Barbir^a, J. Pečarić<sup>b

a</sup> University of Split
^b University of Zagreb

Abstract: In this paper, we consider generalizations of Opial's inequality due to Willett, Godunova, Levin, and Rozanova. Cauchy-type mean-value theorems are proved and used in studying Stolarsky-type means defined by the obtained inequalities. Also, a method of producing $n$-exponentially convex and exponentially convex functions is applied.

Keywords: Willett's inequality, Godunova–Levin's inequality, Rozanova's inequality, Cauchy mean-value theorems, exponential convexity, Stolarsky means.

UDC: 517.272

Received: 10.04.2013

DOI: 10.4213/mzm10560

 English version: Mathematical Notes, 2014, 96:6, 841–854

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