Levinsonova nejednakost

Ljuboja, Žana (2015) Levinsonova nejednakost. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

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 Fans 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.

Item Type: Thesis (Diploma thesis)
Supervisor: Mićić Hot, Jadranka
Date: 2015
Number of Pages: 43
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 01 Apr 2016 09:42
Last Modified: 01 Apr 2016 09:42
URI: http://digre.pmf.unizg.hr/id/eprint/4376

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