Tbilisi Mathematical Journal

Some perturbed trapezoid inequalities for convex, $s$-convex and $tgs$-convex functions and applications

Mevlüt Tunç and Ümmügülsüm Şanal

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In this paper, the Authors establish a new identity for twice differentiable functions. Afterwards some new inequalities are presented related to perturbed trapezoid inequality for the classes of functions whose second derivatives of absolute values are convex, $s$-convex and $tgs$-convex. Last of all, applications to special means have also been presented.

Article information

Tbilisi Math. J., Volume 8, Issue 2 (2015), 87-102.

Received: 27 January 2015
Accepted: 26 May 2015
First available in Project Euclid: 12 June 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26A51: Convexity, generalizations
Secondary: 26D10: Inequalities involving derivatives and differential and integral operators 26D15: Inequalities for sums, series and integrals 26E60: Means [See also 47A64]

Hermite-Hadamard inequalities convex function $s$-convex function $tgs$-convex function perturbed trapezoid inequality means


Tunç, Mevlüt; Şanal, Ümmügülsüm. Some perturbed trapezoid inequalities for convex, $s$-convex and $tgs$-convex functions and applications. Tbilisi Math. J. 8 (2015), no. 2, 87--102. doi:10.1515/tmj-2015-0013. https://projecteuclid.org/euclid.tbilisi/1528769009

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