Simpson and Newton type inequalities for convex functions via newly defined quantum integrals
Hüseyin Budak, Samet Erden, Muhammad Aamir Ali
Abstract
We first establish two new identities, based on the kernel functions with either two section or three sections, involving quantum integrals by using new definition of quantum derivative. Then, some new inequalities related to Simpson's 1/3 formula for convex mappings are provided. In addition, Newton type inequalities, for functions whose quantum derivatives in modulus or their powers are convex, are deduced. We also mention that the results in this work generalize inequalities given in earlier study.
Topics & Concepts
MathematicsQuantumRegular polygonConvex functionType (biology)InequalityPure mathematicsSection (typography)Mathematical analysisAlgebra over a fieldGeometryQuantum mechanicsAdvertisingBusinessPhysicsEcologyBiologyMathematical Inequalities and ApplicationsFunctional Equations Stability ResultsIterative Methods for Nonlinear Equations