On some new trapezoidal inequalities for qϰ2 -quantum integrals via Green function

Muhammad Aamir Ali; Necmettin Alp; Hüseyin Budak; Praveen Agarwal

doi:10.1007/s41478-021-00323-8

On some new trapezoidal inequalities for ^qϰ2 -quantum integrals via Green function

Muhammad Aamir Ali
, Necmettin Alp
, Hüseyin Budak
, Praveen Agarwal

Nonlinear Dynamic Research Centre (NDRC)

Nanjing Normal University
Duzce University
International College of Engineering

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

1 Scopus citations

Abstract

In this paper, we first obtain a new identity for qϰ2-quantum integrals by using Green function, the result is then used to establish some new bounds for the right hand side of qϰ2-Hermite Hadamard inequality. It is also revealed that the results presented in this research transformed into some already proved results by considering the limits as q→ 1 ^- in the newly obtained results.

Original language	English
Pages (from-to)	15-33
Number of pages	19
Journal	Journal of Analysis
Volume	30
Issue number	1
DOIs	https://doi.org/10.1007/s41478-021-00323-8
State	Published - Mar 2022

Keywords

Convex functions
Green function
Hermite–Hadamard inequality
Quantum calculus
q-integral

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10.1007/s41478-021-00323-8

Cite this

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abstract = "In this paper, we first obtain a new identity for qϰ2-quantum integrals by using Green function, the result is then used to establish some new bounds for the right hand side of qϰ2-Hermite Hadamard inequality. It is also revealed that the results presented in this research transformed into some already proved results by considering the limits as q→ 1 - in the newly obtained results.",

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AU - Budak, Hüseyin

AU - Agarwal, Praveen

PY - 2022/3

Y1 - 2022/3

N2 - In this paper, we first obtain a new identity for qϰ2-quantum integrals by using Green function, the result is then used to establish some new bounds for the right hand side of qϰ2-Hermite Hadamard inequality. It is also revealed that the results presented in this research transformed into some already proved results by considering the limits as q→ 1 - in the newly obtained results.

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KW - Convex functions

KW - Green function

KW - Hermite–Hadamard inequality

KW - Quantum calculus

KW - q-integral

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On some new trapezoidal inequalities for ^qϰ2 -quantum integrals via Green function

Abstract

Keywords

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