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master's thesis
Levinsonova nejednakost
Zagreb: University of Zagreb, Faculty of Science, 2015. urn:nbn:hr:217:131257
Ljuboja, Žana
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Ljuboja, Ž. (2015). Levinsonova nejednakost (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:131257

Ljuboja, Žana. "Levinsonova nejednakost." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:131257

Ljuboja, Žana. "Levinsonova nejednakost." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:131257

Ljuboja, Ž. (2015). 'Levinsonova nejednakost', Master's thesis, University of Zagreb, Faculty of Science, accessed 03 April 2025, https://urn.nsk.hr/urn:nbn:hr:217:131257

Ljuboja Ž. Levinsonova nejednakost [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2015 [cited 2025 April 03] Available at: https://urn.nsk.hr/urn:nbn:hr:217:131257

Ž. Ljuboja, "Levinsonova nejednakost", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2015. Available at: https://urn.nsk.hr/urn:nbn:hr:217:131257

Metadata
TitleLevinsonova nejednakost
AuthorŽana Ljuboja
MentorJadranka Mićić Hot (mentor)
Committee memberJadranka Mićić Hot (predsjednik povjerenstva)
Committee memberSanja Varošanec (član povjerenstva)
Committee memberIvica Nakić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2015-11-27, 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... More 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 x3 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. Less
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... More 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 x3 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. Less
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:131257
Study programmeTitle: 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 resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-02-28 13:59:12
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