General Integral Identities and Related Inequalities

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Ova znanstvena monografija daje nov pristup, odnosno metodu izvođenja raznih kvadraturnih formula na jedinstven način, korištenjem integralnih identiteta. Prikazana metoda nadalje omogućava procjenu greške za dobivene kvadraturne formule, što su opet vrlo zanimljivi rezultati. Isto tako, pomoću izvedenih identiteta, dobivene su brojne generalizacije nejednakosti Ostrowskijevog tipa.

The authors first state the fundamental properties of bounded linear operators on a Hilbert space. The main objective of this book is to expose some recent research in the theory of weighted integral and discrete inequalities of Ostrowski type, with emphasis on its various useful applications such as generalizations of classical numerical quadrature rules. Obtained results generalize, refine, unify or sharpen some well-known or previously obtained inequalities. General identities from which the related inequalities are deduced in this book are various kinds of different generalizations of Montgomery identity and Euler integral formula which express expansion of a function in terms of Bernoulli polynomials. This book is intended for researchers in the field of mathematical inequalities, but it can also be used by graduate students and advanced undergraduates.