On some new simpson’s formula type inequalities for convex functions in post-quantum calculus

Miguel J. Vivas-Cortez; Muhammad Aamir Ali; Shahid Qaisar; Ifra Bashir Sial; Sinchai Jansem; Abdul Mateen

doi:10.3390/sym13122419

On some new simpson’s formula type inequalities for convex functions in post-quantum calculus

Miguel J. Vivas-Cortez^*
, Muhammad Aamir Ali^*
, Shahid Qaisar
, Ifra Bashir Sial
, Sinchai Jansem
, Abdul Mateen

^*Corresponding author for this work

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

12 Scopus citations

Abstract

In this work, we prove a new (p, q)-integral identity involving a (p, q)-derivative and (p, q)-integral. The newly established identity is then used to show some new Simpson’s formula type inequalities for (p, q)-differentiable convex functions. Finally, the newly discovered results are shown to be refinements of comparable results in the literature. Analytic inequalities of this type, as well as the techniques used to solve them, have applications in a variety of fields where symmetry is important.

Original language	English
Article number	2419
Journal	Symmetry
Volume	13
Issue number	12
DOIs	https://doi.org/10.3390/sym13122419
State	Published - 14 Dec 2021

Bibliographical note

Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.

Funding

This research was funded by the Science, Research and Innovation Promotion Fund under the Basic Research Plan–Suan Dusit University. Contract no.65-FF-010. Miguel Vivas-Cortez wishes to thank to Dirección de Investigación from Pontificia Universidad Católica del Ecuador. In addition, all the authors wish to thank those appointed to review this article and the editorial team of Symmetry. Funding: This research was funded by the Science, Research and Innovation Promotion Fund under the Basic Research Plan–Suan Dusit University. Contract no.65-FF-010.

Funders
Suan Dusit University

Keywords

Convex functions
Post-quantum calculus
Simpson’s inequalities

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Cite this

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abstract = "In this work, we prove a new (p, q)-integral identity involving a (p, q)-derivative and (p, q)-integral. The newly established identity is then used to show some new Simpson{\textquoteright}s formula type inequalities for (p, q)-differentiable convex functions. Finally, the newly discovered results are shown to be refinements of comparable results in the literature. Analytic inequalities of this type, as well as the techniques used to solve them, have applications in a variety of fields where symmetry is important.",

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AU - Ali, Muhammad Aamir

AU - Qaisar, Shahid

AU - Sial, Ifra Bashir

AU - Jansem, Sinchai

AU - Mateen, Abdul

PY - 2021/12/14

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AB - In this work, we prove a new (p, q)-integral identity involving a (p, q)-derivative and (p, q)-integral. The newly established identity is then used to show some new Simpson’s formula type inequalities for (p, q)-differentiable convex functions. Finally, the newly discovered results are shown to be refinements of comparable results in the literature. Analytic inequalities of this type, as well as the techniques used to solve them, have applications in a variety of fields where symmetry is important.

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KW - Post-quantum calculus

KW - Simpson’s inequalities

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On some new simpson’s formula type inequalities for convex functions in post-quantum calculus

Abstract

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Keywords

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