New post quantum analogues of Ostrowski-type inequalities using new definitions of left–right $(p,q)$-derivatives and definite integrals-Reference-Cited by-同舟云学术

New post quantum analogues of Ostrowski-type inequalities using new definitions of left–right $(p,q)$-derivatives and definite integrals

Published:2020-11-11 Issue:1 Volume:2020 Page:
ISSN:1687-1847
Container-title:Advances in Difference Equations
language:en
Short-container-title:Adv Differ Equ

Author:

Chu Yu-Ming,Awan Muhammad Uzair^ORCID,Talib Sadia,Noor Muhammad Aslam,Noor Khalida Inayat

Abstract

AbstractThe main objective of this paper is to introduce a new more elegant notion of left–right

$(p,q)$

(p,q)-derivative and definite integrals. To show the significance of these concepts, we discuss some of their basic properties. A new generalized

$(p,q)$

(p,q)-integral identity is also obtained. Utilizing this identity as an auxiliary result we then obtain our main results using the concept ofn-polynomial convex functions.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Algebra and Number Theory,Analysis

Link

http://link.springer.com/content/pdf/10.1186/s13662-020-03094-x.pdf

Reference38 articles.

1. Ahmad, B., Alsaedi, A., Nazemi, S.Z., Rezapour, S.: Some existence theorems for fractional integro-differential equations and inclusions with initial and non-separated boundary conditions. Bound. Value Probl. 2014, Article ID 249 (2014)

2. Alp, N., Sarıkaya, M.Z., Kunt, M., İşcan, İ.: q-Hermite–Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions. J. King Saud Univ., Sci. 30(2), 193–203 (2018)

3. Awan, M.U., Akhtar, N., Iftikhar, S., Noor, M.A., Chu, Y.-M.: New Hermite–Hadamard type inequalities for n-polynomial harmonically convex functions. J. Inequal. Appl. 2020, Article ID 125 (2020)

4. Awan, M.U., Talib, S., Chu, Y.-M., Noor, M.A., Noor, K.I.: Some new refinements of Hermite–Hadamard-type inequalities involving $\psi _{k}$-Riemann–Liouville fractional integrals and applications. Math. Probl. Eng. 2020, Article ID 3051920 (2020)

5. Aydogan, M.S., Baleanu, D., Mousalou, A., Rezapour, S.: On high order fractional integro-differential equations including the Caputo–Fabrizio derivative. Bound. Value Probl. 2018, Article ID 90 (2018)

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