engleski

Applications of the weighted Hermite-Hadamard inequality for higher order convex functions in deriving new estimates for various quadrature formulas

The theory of convex function is at its core a theory about comparing arithmetic means (of certain random variables with their composition by a given function). The well known Hermite-Hadamard inequality gives us an estimate of the (integral) mean value of a continuous convex function. Hermite-Hadamard’s inequality was first noticed by Ch. Hermite in 1883 and rediscovered ten years later by J. Hadamard. It is interesting that each of the two sides of Hermite-Hadamard’s inequality characterizes convex functions. In this talk, new estimates for some quadrature rules (integral identities for numerical calculation of the definite integral) are presented using the weighted Hermite-Hadamard inequality for higher order convex functions and weighted version of the integral identity expressed by w-harmonic sequences of functions. Applying obtained results on some special cases of the weight functions new estimates of various classical quadrature formulas are given in several examples.

Hermite-Hadamard’s inequality, Higher Order Convex Function, Harmonic Sequence, Quadrature Formula, Weighted Function

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