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, Kamsing Nonlaopon
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.
Topics & Concepts
MathematicsDifferentiable functionInequalityConvex functionRegular polygonCalculus (dental)Pure mathematicsQuantumDerivative (finance)Applied mathematicsMathematical analysisGeometryQuantum mechanicsPhysicsMedicineDentistryEconomicsFinancial economicsMathematical Inequalities and ApplicationsFunctional Equations Stability ResultsMathematical functions and polynomials