Some New Inequalities on Generalization of Hermite-Hadamard and Bullen Type Inequalities, Applications to Trapezoidal and Midpoint Formula
İmdat Işcan, Tekin Toplu, Fatih Yetgin
Abstract
In this paper, we give a new general identity for differentiable functions. A consequence of the identity is that we obtain some new general inequalities containing all of the Hermite-Hadamard and Bullen type for functions whose derivatives in absolute value at certain power are convex. Some applications to special means of real numbers are also given. Finally, some error estimates for the trapezoidal and midpoint formula are addressed.
Topics & Concepts
MathematicsMidpointHermite polynomialsHadamard transformIdentity (music)Type (biology)GeneralizationPure mathematicsAlgebra over a fieldMathematical analysisGeometryEcologyPhysicsBiologyAcousticsMathematical Inequalities and ApplicationsMathematical functions and polynomials