Quantum Ostrowski-type inequalities for twice quantum differentiable functions in quantum calculus-Reference-Cited by-同舟云学术

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Quantum Ostrowski-type inequalities for twice quantum differentiable functions in quantum calculus

Published:2021-01-01 Issue:1 Volume:19 Page:440-449
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Ali Muhammad Aamir¹,Budak Hüseyin²,Akkurt Abdullah³,Chu Yu-Ming⁴

Affiliation:

1. Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University , Nanjing , China

2. Department of Mathematics, Faculty of Science and Arts, Düzce University , Düzce , Turkey

3. Department of Mathematics, Faculty of Science and Arts, Kahramanmaraş Sütçü İmam University , Kahramanmaraş , Turkey

4. Department of Mathematics, Huzhou University , 313000 , Huzhou , China

Abstract

Abstract In this paper, we first prove an identity for twice quantum differentiable functions. Then, by utilizing the convexity of

∣ D q 2 b f ∣

| {}^{b}D_{q}^{2}\hspace{0.08em}f|

and

∣ D q 2 a f ∣

| {}_{a}D_{q}^{2}\hspace{0.08em}f|

, we establish some quantum Ostrowski inequalities for twice quantum differentiable mappings involving

q a

{q}_{a}

and

q b

{q}^{b}

-quantum integrals. The results presented here are the generalization of already published ones.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2021-0020/pdf

Reference42 articles.

1. A. M. Ostrowski, Über die absolutabweichung einer differentiebaren funktion von ihrem integralmitelwert, Comment. Math. Helv. 10 (1938), 226–227.

2. H. Budak, M. Z. Sarikaya, and S. S. Dragomir, Some perturbed Ostrowski-type inequalities for twice differentiable functions, in: P. Agarwal, S. Dragomir, M. Jleli, B. Samet (eds.), Advances in Mathematical Inequalities and Applications, Trends in Mathematics, Birkhäuser, Singapore, 2018, pp. 279–294.

3. Y.-M. Chu, M. U. Awan, S. Talib, M. A. Noor, and K. I. Noor, New post quantum analogues of Ostrowski-type inequalities using new definitions of left-right (p,q)-derivatives and definite integrals, Adv. Difference Equ. 2020 (2020), 634, https://doi.org/10.1186/s13662-020-03094-x.

4. S. S. Dragomir, On the Ostrowski’s integral inequality for mappings with bounded variation and applications, Math. Ineq. Appl. 4 (2001), no. 1, 59–66

5. S. S. Dragomir, The Ostrowski’s integral inequality for Lipschitzian mappings and applications, Comput. Math. Appl. 38 (1999), no. 11–12, 33–37.

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