New Simpson’s Type Estimates for Two Newly Defined Quantum Integrals

Muhammad Raees; Matloob Anwar; Miguel Vivas-Cortez; Artion Kashuri; Muhammad Samraiz; Gauhar Rahman

doi:10.3390/sym14030548

New Simpson’s Type Estimates for Two Newly Defined Quantum Integrals

Muhammad Raees
, Matloob Anwar
, Miguel Vivas-Cortez^*
, Artion Kashuri
, Muhammad Samraiz
, Gauhar Rahman

^*Autor correspondiente de este trabajo

Producción científica: Revista › Artículo › revisión exhaustiva

4 Citas (Scopus)

Resumen

In this paper, we give some correct quantum type Simpson’s inequalities via the application of q-Hölder’s inequality. The inequalities of this study are compatible with famous Simpson’s 1/8 and 3/8 quadrature rules for four and six panels, respectively. Several special cases from our results are discussed in detail. A counter example is presented to explain the limitation of Hölder’s inequality in the quantum framework.

Idioma original	Inglés
Número de artículo	548
Publicación	Symmetry
Volumen	14
N.º	3
DOI	https://doi.org/10.3390/sym14030548
Estado	Publicada - 8 mar 2022

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Publisher Copyright:
© 2022 by the authors. Licensee MDPI, Basel, Switzerland.

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title = "New Simpson{\textquoteright}s Type Estimates for Two Newly Defined Quantum Integrals",

abstract = "In this paper, we give some correct quantum type Simpson{\textquoteright}s inequalities via the application of q-H{\"o}lder{\textquoteright}s inequality. The inequalities of this study are compatible with famous Simpson{\textquoteright}s 1/8 and 3/8 quadrature rules for four and six panels, respectively. Several special cases from our results are discussed in detail. A counter example is presented to explain the limitation of H{\"o}lder{\textquoteright}s inequality in the quantum framework.",

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author = "Muhammad Raees and Matloob Anwar and Miguel Vivas-Cortez and Artion Kashuri and Muhammad Samraiz and Gauhar Rahman",

note = "Publisher Copyright: {\textcopyright} 2022 by the authors. Licensee MDPI, Basel, Switzerland.",

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AU - Raees, Muhammad

AU - Anwar, Matloob

AU - Vivas-Cortez, Miguel

AU - Kashuri, Artion

AU - Samraiz, Muhammad

AU - Rahman, Gauhar

PY - 2022/3/8

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N2 - In this paper, we give some correct quantum type Simpson’s inequalities via the application of q-Hölder’s inequality. The inequalities of this study are compatible with famous Simpson’s 1/8 and 3/8 quadrature rules for four and six panels, respectively. Several special cases from our results are discussed in detail. A counter example is presented to explain the limitation of Hölder’s inequality in the quantum framework.

AB - In this paper, we give some correct quantum type Simpson’s inequalities via the application of q-Hölder’s inequality. The inequalities of this study are compatible with famous Simpson’s 1/8 and 3/8 quadrature rules for four and six panels, respectively. Several special cases from our results are discussed in detail. A counter example is presented to explain the limitation of Hölder’s inequality in the quantum framework.

KW - Convex function

KW - Q-Hölder’s inequality

KW - Quantum derivatives

KW - Quantum integrals

KW - Simpson’s inequality

UR - https://www.scopus.com/pages/publications/85126459799

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