Jedna generalizacija konveksnih funkcija

master's thesis

• Author: Ivana Mrvičić
• Mentor: Sanja Varošanec (mentor)
• Committee member: Sanja Varošanec (predsjednik povjerenstva)
• Committee member: Ivica Nakić (član povjerenstva)
• Committee member: Vedran Krčadinac (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 opisan je jedan način poopćenja pojma konveksnih funkcija koji su opisali Hudzik i Maligranda 1994. godine. Rad se sastoji od tri poglavlja. U uvodu je ukratko opisana tema i cilj rada. Prvo poglavlje sadrži definicije i svojstva s-konveksnih funkcija u prvom i drugom smislu. U drugom poglavlju dokazani su rezultati samo za s-konveksne funkcije u drugom smislu kao što su Jensenova i Hermite-Hadamardova nejednakost, te su dane različite ocjene za razlike lijeve i desne strane Hermite-Hadamardove nejednakosti. U trećem poglavlju izloženi su rezultati za s-konveksne funkcije u prvom smislu.

Abstract (english)

In this thesis we describe one generalization of convex function which was introduced by Hudzik and Maligranda in 1994. The thesis consists of three chapters. In the first chapter we give definitions and some properties of s-convex functions in the first and the second sense. In the second chapter results for s-convex functions in the second sense are proven such as Jensen’s and HermiteHadamard’s inequality. Also there are given different estimates for differences between the left-hand and the right-hand sides of Hermite-Hadamard’s inequality. In the third chapter the results for s-convex functions in the first sense are given.

• Keywords: poopćenje pojma konveksnih funkcija; s-konveksne funkcije; Hermite-Hadamardova nejednakost
• Keywords (english): generalization of convex function; s-convex functions; Hermite-Hadamard’s inequality
• Language: croatian
• URN:NBN: urn:nbn:hr:217:097634
• 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: 2019-01-25 13:00:51