Quantum Hermite–Hadamard-type inequalities for functions with convex absolute values of second qb -derivatives

Muhammad Aamir Ali; Hüseyin Budak; Mujahid Abbas; Yu Ming Chu

doi:10.1186/s13662-020-03163-1

Quantum Hermite–Hadamard-type inequalities for functions with convex absolute values of second q^b -derivatives

Muhammad Aamir Ali
, Hüseyin Budak
, Mujahid Abbas
, Yu Ming Chu

Research output: Contribution to journal › Article › peer-review

66 Citations (Scopus)

Abstract

In this paper, we obtain Hermite–Hadamard-type inequalities of convex functions by applying the notion of q^b-integral. We prove some new inequalities related with right-hand sides of q^b-Hermite–Hadamard inequalities for differentiable functions with convex absolute values of second derivatives. The results presented in this paper are a unification and generalization of the comparable results in the literature on Hermite–Hadamard inequalities.

Original language	English
Article number	7
Journal	Advances in Difference Equations
Volume	2021
Issue number	1
DOIs	https://doi.org/10.1186/s13662-020-03163-1
Publication status	Published - Dec 2021
Externally published	Yes

Keywords

Convex function
Hermite–Hadamard inequality
q-integral
Quantum calculus

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Applied Mathematics

Access to Document

10.1186/s13662-020-03163-1

Cite this

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abstract = "In this paper, we obtain Hermite–Hadamard-type inequalities of convex functions by applying the notion of qb-integral. We prove some new inequalities related with right-hand sides of qb-Hermite–Hadamard inequalities for differentiable functions with convex absolute values of second derivatives. The results presented in this paper are a unification and generalization of the comparable results in the literature on Hermite–Hadamard inequalities.",

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AU - Ali, Muhammad Aamir

AU - Budak, Hüseyin

AU - Abbas, Mujahid

AU - Chu, Yu Ming

PY - 2021/12

Y1 - 2021/12

N2 - In this paper, we obtain Hermite–Hadamard-type inequalities of convex functions by applying the notion of qb-integral. We prove some new inequalities related with right-hand sides of qb-Hermite–Hadamard inequalities for differentiable functions with convex absolute values of second derivatives. The results presented in this paper are a unification and generalization of the comparable results in the literature on Hermite–Hadamard inequalities.

AB - In this paper, we obtain Hermite–Hadamard-type inequalities of convex functions by applying the notion of qb-integral. We prove some new inequalities related with right-hand sides of qb-Hermite–Hadamard inequalities for differentiable functions with convex absolute values of second derivatives. The results presented in this paper are a unification and generalization of the comparable results in the literature on Hermite–Hadamard inequalities.

KW - Convex function

KW - Hermite–Hadamard inequality

KW - q-integral

KW - Quantum calculus

UR - https://www.scopus.com/pages/publications/85098854601

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DO - 10.1186/s13662-020-03163-1

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