Euler integral identity, quadrature formulae and error estimations

Važna napomena:
Cijena od 24,55 € vrijedi SAMO za krajnjeg kupca.

Glavna motivacija za nastajanje ove knjige jest prikaz proširenja, poboljšanja i inačica triju poznatih nejednakosti matematičke analize. To su Hermite-Hadamardova nejednakost koja vrijedi za konveksne funkcije te nejednakost Ostrowskog i Iyengarova nejednakost koje vrijede za L−Lipschitzove funkcije. Kroz cijelu knjigu protežu se generalizacije nejednakosti Ostrowskog, dok se inačice Hermite-Hadamardove nejednakosti prikazuju za određene parove kvadraturnih formula, tzv. dualnih formula. Poboljšanja ove nejednakosti izvedena su u smislu Bullenove nejednakosti koja vrijedi za funkcije čija je n−ta derivacija konveksna funkcija.

The book contains generalizations of many classical quadrature formulas such as Simpson, dual Simpson, Maclaurin, Gauss, Lobatto and Radau. The specific feature of this book is that a unique method is used. This method is based on the Euler integral identities expressing expansion of a function in Bernoulli polynomials, proved by V. I. Krylov as a generalization of the first and the second Euler-Maclaurin sum formula. Mostly as error estimates, the book presents some aspects of generalizations, refinements and variants of four famous inequalities: the Hermite-Hadamard, the Ostrowski, the Bullen and the Iyengar inequality, which is an exception. Although related to the Hermite-Hadamard inequality in the same way as the Ostrowski inequality, Iyengar type inequalities are, it seems, beyond the reach of the method presented in this book. This is the reason why generalizations of the Iyengar inequality are given in the Addendum.