A Qualitative Study of Hermite--Hadamard Inequality

Abstract

This investigation centers to bring into the spotlight some new and generalized Hermite– Hadamard inequalities in the casings of old classical calculus, fractional calculus, quantum calculus and furthermore a few ramifications in local calculus. This dissertation begins with the prologue to the hypothesis of convexity, some essential and generalized fractional integrals, q-differentiation and integration and a few fundamentals about local calculus. Hermite–Hadamard inequalities through approximately convex functions and its including classes are created. An exceptionally broad vital portrayal for Hermite–Hadamard inequality and its weighted partner Fejér–Hermite–Hadamard inequality are set up. The error assessment type results are likewise demonstrated. Hermite–Hadamard inequalities for (p1, h1)- (p2, h2)-convex functions on the coordinates on the rectangle in the plane are additionally settled. Some inequalities for twice differentiable m-convex functions are being developed for quantum integrals. Besides, by applying the thought of local calculus and generalized strongly m-convexity an inequality of Ostrowski type is created and its applications for numerical methods and error formula are talked about