On New Estimates of q-Hermite–Hadamard Inequalities with Applications in Quantum Calculus
Saowaluck Chasreechai, Muhammad Aamir Ali, Muhammad Amir Ashraf, Thanin Sitthiwirattham, Sina Etemad, Manuel De la Sen, Shahram Rezapour
Abstract
In this paper, we first establish two quantum integral (q-integral) identities with the help of derivatives and integrals of the quantum types. Then, we prove some new q-midpoint and q-trapezoidal estimates for the newly established q-Hermite-Hadamard inequality (involving left and right integrals proved by Bermudo et al.) under q-differentiable convex functions. Finally, we provide some examples to illustrate the validity of newly obtained quantum inequalities.
Topics & Concepts
MathematicsMidpointHadamard transformHermite polynomialsDifferentiable functionQuantumPure mathematicsConvex functionInequalityRegular polygonCalculus (dental)Mathematical analysisQuantum mechanicsPhysicsGeometryMedicineDentistryMathematical Inequalities and ApplicationsMathematical functions and polynomials