Funkcionalne jednadžbe pridružene nekim teoremima srednje vrijednosti

master's thesis

• Author: Daria Grozdek
• Mentor: Ljiljana Arambašić (mentor)
• Committee member: Ljiljana Arambašić (predsjednik povjerenstva)
• Committee member: Damir Bakić (član povjerenstva)
• Committee member: Boris Muha (član povjerenstva)
• Committee member: Zvonko Čerin (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-09-23, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu proučavamo funkcionalne jednadžbe motivirane određenim teoremima srednje vrijednosti. U prvom poglavlju opisujemo neke metode rješavanja funkcionalnih jednadžbi, te detaljno proučavamo linearnu i eksponencijalnu Cauchyjevu funkcionalnu jednadžbu. U drugom poglavlju bavimo se teoremima srednje vrijednosti - Rolleovim, Lagrangeovim, Cauchyjevim i Pompeiuovim. Osim dokaza i geometrijske interpretacije pojedinog teorema, dajemo i nekoliko primjera zadataka u čijim se rješenjima primjenjuje Lagrangeov teorem. U trećem poglavlju proučavamo funkcionalne jednadžbe povezane s Lagrangeovim i Pompeiuovim teoremima srednje vrijednosti.

Abstract (english)

In this graduate thesis we examine functional equations motivated by certain mean value theorems. In the first chapter we describe some methods of solving functional equations, and thoroughly examine Cauchy’s linear and exponential functional equations. In the second chapter we examine the mean value theorems - Rolle’s, Lagrange’s, Cauchy’s and Pompeiu’s. Except for the proofs and geometrical interpretations of all theorems, we give some examples solved by using Lagrange’s mean value theorem. In the third chapter we study functional equations associated with Lagrange’s and Pompeiu’s mean value theorem.

• Keywords: funkcionalne jednadžbe; Cauchyjeva funkcionalna jednadžba; Rolleov teorem srednje vrijednosti; Lagrangeov teorem srednje vrijednosti; Cauchyjev teorem srednje vrijednosti; Pompeiuov teorem srednje vrijednosti
• Keywords (english): functional equations; Cauchy’s functional equations; Rolle’s mean value theorem; Lagrange’s mean value theorem; Cauchy’s mean value theorem; Pompeiu’s mean value theorem
• Language: croatian
• URN:NBN: urn:nbn:hr:217:020949
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Access restricted to students and staff of home institution
• Created on: 2019-01-28 14:41:34