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master's thesis
Hosszúova funkcijska jednadžba
Zagreb: University of Zagreb, Faculty of Science, 2018. urn:nbn:hr:217:148633
Ivanković, Nikolina
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Ivanković, N. (2018). Hosszúova funkcijska jednadžba (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:148633

Ivanković, Nikolina. "Hosszúova funkcijska jednadžba." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:148633

Ivanković, Nikolina. "Hosszúova funkcijska jednadžba." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:148633

Ivanković, N. (2018). 'Hosszúova funkcijska jednadžba', Master's thesis, University of Zagreb, Faculty of Science, accessed 27 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:148633

Ivanković N. Hosszúova funkcijska jednadžba [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2018 [cited 2024 November 27] Available at: https://urn.nsk.hr/urn:nbn:hr:217:148633

N. Ivanković, "Hosszúova funkcijska jednadžba", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:217:148633

Metadata
TitleHosszúova funkcijska jednadžba
AuthorNikolina Ivanković
MentorDijana Ilišević (mentor)
Committee memberDijana Ilišević (predsjednik povjerenstva)
Committee memberIlja Gogić (član povjerenstva)
Committee memberSlaven Kožić (član povjerenstva)
Committee memberVjekoslav Kovač (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2018-09-26, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Hosszúova funkcijska jednadžba je jednadžba oblika \[f(x+y-xy)+f(xy)=f(x)+f(y), \qquad x,y \in \mathbb{R}\] Glavninu ovog rada predstavlja rješenje Hosszúove funkcijske jednadžbe i dokaz njezine stabilnosti, te rješenje i stabilnost njezine poopćene varijante \[f(x+y-\alpha xy)+g(xy)=h(x)+k(y), \qquad x,y \in \mathbb{R}.\] Dokazano je da je svako rjesenje Hosszúove funkcijske jednadžbe oblika \[f(x)=A(x)+ a,\] pri čemu je \(A\) aditivno preslikavanje i \(a\) realna konstanta. Pored toga prikazana je i veza Hosszúove funkcijske jednadžbe s nekim drugim poznatim funkcijskim jednadžbama. Konkretno, dan je dokaz ekvivalentnosti Hosszúove i Jensenove funkcijske jednadžbe te Hosszúove i tzv. Hosszú-Jensenove funkcijske jednadžbe.
Abstract (english)
Hosszú functional equation is an equation of the form \[f(x+y-xy)+f(xy)=f(x)+f(y), \qquad x,y \in \mathbb{R}\] The main goal of this thesis is to present the solution of the Hosszú functional equation and the proof of its stability, as well as the solution and stability of its generalization, the functional equation \[f(x+y-\alpha xy)+g(xy)=h(x)+k(y), \qquad x,y \in \mathbb{R}.\] It is proved that every solution of the Hosszú functional equation is of the form \[f(x)=A(x)+ a,\] where \(A\) is an additive function and \(a\) is an arbitrary constant. Furthermore, relations to some other well-known functional equations have also been mentioned. Specifically, a proof of the equivalency of the Hosszú and the Jensen functional equation is also presented, as well as the equivalency of the Hosszú and the so-called Hosszú-Jensen functional equation.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:148633
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 on2019-05-09 13:23:39