Levinsonova nejednakost

master's thesis

• Author: Žana Ljuboja
• Mentor: Jadranka Mićić Hot (mentor)
• Committee member: Jadranka Mićić Hot (predsjednik povjerenstva)
• Committee member: Sanja Varošanec (član povjerenstva)
• Committee member: Ivica Nakić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-11-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu bavimo se Levinsonovom nejednakošću i njenim generalizacijama. Rad se sastoji od pet poglavlja. U Poglavlju 1 opisan je život američkog matematičara Normana Levinsona i njegovi najveći doprinosi te navodimo kako je Levinson dobio generalizaciju Ky Fanove nejednakosti koju danas nazivamo Levinsonova nejednakost. U Poglavlju 2 govorimo o \(n\)-konveksnim funkcijama, specijalno 3-konveksnim funkcijama za koje vrijedi Levinsonova nejednakost. U Poglavlju 3 govorimo o promjeni uvjeta za točke. Konkretnije, spominjemo rezultate u kojima se razmatra Levinsonova nejednakost uz nešto slabije uvjete na izbor točaka. U Poglavlju 4 dajemo rezultat u kojem je razlika lijeve i desne strane Levinsonove nejednakosti izražena kao produkt istovrsne razlike za polinom \(x^3\) i treće derivacije funkcije \(f\) u jednoj točki domene. U Poglavlju 5 bavimo se promjenama uvjeta za funkciju. Pokazujemo da Levinsonova nejednakost vrijedi za funkcije koje su 3-konveksne u točki.

Abstract (english)

In this paper we consider with Levinson’s inequality and its generalizations. The work consists of five chapters. In Chapter 1 we describe the life of an American mathematician Norman Levinson and his greatest contribution and show how Levinson proved generalization Ky Fan's inequality which we called Levinson’s inequality. In Chapter 2, we talk about the \(n\)-convex functions, particularly, about 3-convex functions for which Levinson’s inequality also holds. In Chapter 3 we consider changing of conditions of points. In fact, we give results connected with Levinson’s inequality with weak assumptions on points. In Chapter 4 we give a result in which the difference between the left-hand and the right-hand sides of Levinson’s inequality is expressed as a product equivalent to the difference polynomial \(x^3\) and third derivatives of \(f\) at one point of domain. In Chapter 5 we change assumptions of the function. Namely, we prove that Levinson’s inequality holds for functions which are 3-convex at a point.

• Keywords: Levinsonova nejednakost; Ky Fanova nejednakost
• Keywords (english): Levinson's inequality; Ky Fan inequality
• Language: croatian
• URN:NBN: urn:nbn:hr:217:131257
• 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: Open access
• Created on: 2019-02-28 13:59:12