Kvaziaritmetičke sredine

Lovrić, Sanja (2016) Kvaziaritmetičke sredine. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

This graduate thesis studies quasiarithmetic means. The paper consists of four chapters. The first chapter deals with the concept of convexity. Numerous properties of convex functions are proven and examples of convex functions are provided. The second chapter studies discrete and integral form of Jensen’s and Hermite-Hadamard’s inequalities. These inequalities are used for comparison of mathematical means. The third chapter examines arithmetic, geometric and harmonic means and basic integral means: arithmetic, identric and logarithmic. At the end of the chapter all aforementioned means are sorted by size. The fourth chapter deals with discrete and integral quasiarithmetic means. The basic theorem which refers to order of quasiarithmetic means is proven. End of the paper introduces power means as a special case of discrete and logarithmic means as a special case of integral quasiarithmetic means.

Item Type: Thesis (Diploma thesis)
Supervisor: Pavić, Zlatko and Varošanec, Sanja
Date: 2016
Number of Pages: 44
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 19 May 2016 10:51
Last Modified: 19 May 2016 10:51
URI: http://digre.pmf.unizg.hr/id/eprint/4841

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