New quantum boundaries for quantum Simpson’s and quantum Newton’s type inequalities for preinvex functions

Muhammad Aamir Ali; Mujahid Abbas; Hüseyin Budak; Praveen Agarwal; Ghulam Murtaza; Yu Ming Chu

doi:10.1186/s13662-021-03226-x

New quantum boundaries for quantum Simpson’s and quantum Newton’s type inequalities for preinvex functions

Muhammad Aamir Ali
, Mujahid Abbas
, Hüseyin Budak
, Praveen Agarwal
, Ghulam Murtaza
, Yu Ming Chu

Nanjing Normal University
Government College University Lahore
Duzce University
International College of Engineering
University of Management and Technology
Huzhou University

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

86 Scopus citations

Abstract

In this research, we derive two generalized integral identities involving the qϰ2-quantum integrals and quantum numbers, the results are then used to establish some new quantum boundaries for quantum Simpson’s and quantum Newton’s inequalities for q-differentiable preinvex functions. Moreover, we obtain some new and known Simpson’s and Newton’s type inequalities by considering the limit q→ 1 ⁻ in the key results of this paper.

Original language	English
Article number	64
Journal	Advances in Difference Equations
Volume	2021
Issue number	1
DOIs	https://doi.org/10.1186/s13662-021-03226-x
State	Published - Dec 2021
Externally published	Yes

Keywords

Integral inequalities
Preinvex functions
Quantum calculus
Simpson’s 1/3 formula
Simpson’s 3/8 formula

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title = "New quantum boundaries for quantum Simpson{\textquoteright}s and quantum Newton{\textquoteright}s type inequalities for preinvex functions",

abstract = "In this research, we derive two generalized integral identities involving the qϰ2-quantum integrals and quantum numbers, the results are then used to establish some new quantum boundaries for quantum Simpson{\textquoteright}s and quantum Newton{\textquoteright}s inequalities for q-differentiable preinvex functions. Moreover, we obtain some new and known Simpson{\textquoteright}s and Newton{\textquoteright}s type inequalities by considering the limit q→ 1 − in the key results of this paper.",

keywords = "Integral inequalities, Preinvex functions, Quantum calculus, Simpson{\textquoteright}s 1/3 formula, Simpson{\textquoteright}s 3/8 formula",

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T1 - New quantum boundaries for quantum Simpson’s and quantum Newton’s type inequalities for preinvex functions

AU - Ali, Muhammad Aamir

AU - Abbas, Mujahid

AU - Budak, Hüseyin

AU - Agarwal, Praveen

AU - Murtaza, Ghulam

AU - Chu, Yu Ming

PY - 2021/12

Y1 - 2021/12

N2 - In this research, we derive two generalized integral identities involving the qϰ2-quantum integrals and quantum numbers, the results are then used to establish some new quantum boundaries for quantum Simpson’s and quantum Newton’s inequalities for q-differentiable preinvex functions. Moreover, we obtain some new and known Simpson’s and Newton’s type inequalities by considering the limit q→ 1 − in the key results of this paper.

AB - In this research, we derive two generalized integral identities involving the qϰ2-quantum integrals and quantum numbers, the results are then used to establish some new quantum boundaries for quantum Simpson’s and quantum Newton’s inequalities for q-differentiable preinvex functions. Moreover, we obtain some new and known Simpson’s and Newton’s type inequalities by considering the limit q→ 1 − in the key results of this paper.

KW - Integral inequalities

KW - Preinvex functions

KW - Quantum calculus

KW - Simpson’s 1/3 formula

KW - Simpson’s 3/8 formula

UR - https://www.scopus.com/pages/publications/85099747063

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DO - 10.1186/s13662-021-03226-x

M3 - Article

AN - SCOPUS:85099747063

SN - 1687-1839

VL - 2021

JO - Advances in Difference Equations

JF - Advances in Difference Equations

IS - 1

M1 - 64

ER -

New quantum boundaries for quantum Simpson’s and quantum Newton’s type inequalities for preinvex functions

Abstract

Keywords

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