On Some Generalized Simpson’s and Newton’s Inequalities for ( α, m )-Convex Functions in q -Calculus

Ifra Bashir Sial, Sun Mei, Muhammad Aamir Ali and Kamsing Nonlaopon
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Ifra Bashir Sial: School of Mathematics Science, Jiangsu University, Zhenjiang 212114, China
Sun Mei: School of Mathematics Science, Jiangsu University, Zhenjiang 212114, China
Muhammad Aamir Ali: Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
Kamsing Nonlaopon: Department of Mathematics, Faculty of Science and Arts, Khon Kaen University, Khon Kaen 40002, Thailand

Mathematics, 2021, vol. 9, issue 24, 1-14

Abstract: In this paper, we first establish two right-quantum integral equalities involving a right-quantum derivative and a parameter m ∈ 0 , 1 . Then, we prove modified versions of Simpson’s and Newton’s type inequalities using established equalities for right-quantum differentiable α , m -convex functions. The newly developed inequalities are also proven to be expansions of comparable inequalities found in the literature.

Keywords: Simpson’s inequalities; Newton’s inequalities; quantum calculus; ( ? , m )-convex functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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