Tbilisi Mathematical Journal
- Tbilisi Math. J.
- Volume 8, Issue 2 (2015), 87-102.
Some perturbed trapezoid inequalities for convex, $s$-convex and $tgs$-convex functions and applications
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.
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
Permanent link to this document
Digital Object Identifier
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]
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