HERMITE-HADAMARD TYPE INEQUALITIES FOR QUASI-CONVEX FUNCTIONS VIA IMPROVED POWER-MEAN INEQUALITY

In this paper, by using power-mean and improved power-mean integral inequality and an general identity for differentiable functions we can get new estimates on integral inequalities for functions whose derivatives in absolute value at certain power are quasi-convex functions. It is proved that the r...

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Bibliographic Details
Published in:TWMS journal of applied and engineering mathematics 2021-01, Vol.11 (1), p.194
Main Author: Kadakal, Mahir
Format: Article
Language:English
Subjects:
Convex analysis
Equality
Inequalities
Inequality
Integrals
Real numbers
Online Access:Get full text
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Summary:In this paper, by using power-mean and improved power-mean integral inequality and an general identity for differentiable functions we can get new estimates on integral inequalities for functions whose derivatives in absolute value at certain power are quasi-convex functions. It is proved that the result obtained improved power-mean integral inequality is better than the result obtained power-mean inequality. Some applications to special means of real numbers are also given. Keywords: Hermite-Hadamard inequality, improved power-mean inequality, midpoint type inequality, convex function, quasi-convex unctions. AMS Subject Classification: 26D15, 26E70
ISSN:2146-1147
2146-1147