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 3convex 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 lefthand and the righthand 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 3convex 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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