Research Interests

Mathematical Inequalities and Applications

Degrees

• PhD, 2009, Department of Mathematics, University of Zagreb
• MSc, 2005, Department of Mathematics, University of Zagreb
• BSc, 2001, Department of Mathematics, University of Osijek

Publications

1. S. Kovač, J. Pečarić, M. Ribičić Penava, Weighted Montgomery identity and weighted Hadamard inequalities, Journal of Mathematical Inequalities 18/1 (2024), 271-285
2. J. Barić, Lj. Kvesić, J. Pečarić, M. Ribičić Penava, Estimates on some quadrature rules via weighted Hermite-Hadamard inequality , Applicable Analysis and Discrete Mathematics 16/1 (2022), 232-245
3. J. Barić, Lj. Kvesić, J. Pečarić, M. Ribičić Penava, Fejér type inequalities for higher order convex functions and quadrature formulae, Aequationes mathematicae 96/2 (2022), 417-430
4. M. Ribičić Penava, Hermite–Hadamard–Fejér-Type Inequalities and Weighted Three-Point Quadrature Formulae, Mathematics 9/15 (2021), 1-14
5. J. Barić, Lj. Kvesić, J. Pečarić, M. Ribičić Penava, New bounds for generalized Taylor expansions, Mathematical Inequalities and Applications 24/4 (2021), 993-999
6. M. Ribičić Penava, Weighted integral inequalities of Euler-Grüss type with applications, Transactions of A. Razmadze Mathematical Institute 175/3 (2021), 401-409
7. Lj. Kvesić, J. Pečarić, M. Ribičić Penava, Generalizations of Ostrowski type inequalities via Hermite polynomials, Journal of Inequalities and Applications 176 (2020), 1-14
8. J. Pečarić, M. Ribičić Penava, Weighted Ostrowski and Gruss type inequalities, Journal of Inequalities and Special Functions 11/1 (2020), 12-23
9. J. Pečarić, M. Ribičić Penava, Bounds for the Chebyshev functional and corrected four-point quadrature formulae of Euler type, Asian-European Journal of Mathematics 9/4 (2017), 1-12
10. J. Pečarić, M. Ribičić Penava, A. Vukelić, Bounds for the Chebyshev functional and applications to the weighted integral formulae, Applied mathematics and computation 268 (2015), 957-965
11. K.M. Awan, J. Pečarić, M. Ribičić Penava, Companion inequalities to Ostrowski-Grϋss type inequality and applications, Turkish Journal of Mathematics 39 (2015), 228-234
12. K.M. Awan, J. Pečarić, M. Ribičić Penava, New estimations of the remainder in three-point and four-point quadrature formulae via the Chebyshev functional, Proceedings of A. Razmadze Mathematical Institute 167 (2015), 3-18
13. M. Klaričić Bakula, J. Pečarić, M. Ribičić Penava, A. Vukelić, New estimations of the remainder in three-point quadrature formulae of Euler type, Journal of Mathematical Inequalities 9/4 (2015), 1143-1156
14. M. Klaričić Bakula, J. Pečarić, M. Ribičić Penava, A. Vukelić, Some Grϋss type inequalities and corrected three-point quadrature formulae of Euler type, Journal of Inequalities and Applications 76 (2015), 1-14
15. M. Klaričić Bakula, J. Pečarić, M. Ribičić Penava, A. Vukelić, Some inequalities for the Čebyšev functional and general four-point quadrature formulae of Euler type, Matematički bilten 38/2 (2014), 69-80
16. M. Klaričić Bakula, J. Pečarić, M. Ribičić Penava, General quadrature formulae based on the weighted Montgomery identity and related inequalities, Rad HAZU, Matematičke znanosti. 17 (2013), 139-150
17. J. Pečarić, M. Ribičić Penava, Sharp integral inequalities based on a general four-point quadrature formula via a generalization of the Montgomery identity, International Journal of Mathematics and Mathematical Sciences 2012 (2012)
18. J. Pečarić, M. Ribičić Penava, Sharp integral inequalities based on general three-point formula, Annals of the University of Craiova, Mathematics and Computer Science Series 39/2 (2012), 132-147
19. M. Klaričić Bakula, M. Ribičić Penava, General four-point quadrature formulae with applications for α-L-Hölder type functions , Journal of Mathematical Inequalities 3/3 (2009), 427-436
20. A. Aglić Aljinović, J. Pečarić, M. Ribičić Penava, Sharp integral inequalities based on general two-point formula via an extension of Montgomery identity, ANZIAM Journal 51/01 (2009), 67-101
21. J. Pečarić, M. Ribičić Penava, A. Vukelić, Euler's method for weighted integral formulae, Applied mathematics and computation 206/1 (2008), 445-456
22. M. Klaričić Bakula, J. Pečarić, M. Ribičić Penava, General three-point quadrature formulae with applications for α-L-Hölder type functions , Journal of Mathematical Inequalities 2/3 (2008), 343-361
23. M. Klaričić Bakula, J. Pečarić, M. Ribičić Penava, Companion inequalities to Jensen's inequality for m-convex and (α,m)-convex functions , Journal of Inequalities in Pure and Applied Mathematics 7/5 (2006), 1-32

1. D. Jukić, D. Marković, M. Ribičić Penava, A. Krajina, On the choice of initial approximation of the least squares estimate in some growth models of exponential type, 9th International Conference on Operational Research KOI 2002, Trogir, 2002, 47-55

1. M. Ribičić Penava, N. Ujić, Jacobijevi polinomi, Osječki matematički list 22/1 (2022), 1-18
   Abstract

   U ovome radu prezentirani su Jacobijevi polinomi, njihova osnovna svojstva i specijalni slučajevi kao što su Legendreovi, Čebiševljevi i Gegenbauerovi polinomi. Osim toga, pokazana je primjena Jacobijevih polinoma pri računanju momenata nekih neprekidnih slučajnih varijabli.
2. D. Brajković Zorić, I. Kuzmanović Ivičić, M. Ribičić Penava, Matematičko natjecanje MathOS cup, Osječki matematički list 22/1 (2022), 81-89
   Abstract

   Cilj ovoga rada je predstaviti timsko natjecanje MathOS cup te dati pregled odabranih zadataka s rješenjima iz drugog kruga natjecanja MathOS cup 2022.
3. T. Milas, M. Ribičić Penava, K. Sabo, Primjene gama funkcije, Osječki matematički list 21/1 (2021), 1-18
   Abstract

   U ovom je radu ukratko opisana gama funkcija te je stavljen naglasak na neke njezine primjene u različitim područjima matematike. Opisane su primjene u geometriji, vjerojatnosti (momenti nekih neprekidnih slučajnih varijabli te gama distribucija) te u teoriji Laplaceovih transformacija.
4. M. Ribičić Penava, A. Nuić, Bernoullijevi polinomi, Osječki matematički list 18/2 (2018), 147-157
   Abstract

   U ovome radu prezentirana su neka osnovna svojstva Bernoullijevih brojeva i Bernoullijevih polinoma. Razmatrane su primjene Bernoullijevih brojeva i Bernoullijevih polinoma pri računanju suma potencija prvih n prirodnih brojeva, pri razvoju funkcija u Taylorov red te kod numeričke integracije.
5. M. Ribičić Penava, K. Bošnjak, Jensenova nejednakost i nejednakosti izvedene iz nje, Osječki matematički list 16/1 (2016), 15-25
   Abstract

   U ovom radu prezentiran je težinski oblik diskretne Jensenove nejednakosti te je pokazano kako iz Jensenove nejednakosti slijedi čitav niz drugih važnih nejednakosti kao što su nejednakosti međžu sredinama, Youngova nejednakost, Cauchyjeva nejednakost, Hölderova nejednakost te nejednakost Minkowskog.
6. M. Ribičić Penava, D. Škrobar, Gama i beta funkcije, Osječki matematički list 15/2 (2015), 93-111
   Abstract

   U ovom radu prezentirana su neka osnovna svojstva gama i beta funkcija te iskazan Bohr-Mollerupov teorem. Osim toga, razmatrane su primjene gama i beta funkcija pri računanju integrala koje nije moguće izračunati uobičajenim metodama.

1. A. Aglić Aljinović, A. Čivljak, S. Kovač, J. Pečarić, M. Ribičić Penava, General Integral Identities and Related Inequalities, Element, Zagreb, 2013.

Projects

• GAMe-based learning in MAthematics (GAMMA)

Erasmus+ project (Key action: KA2 – Cooperation for innovation and the exchange of good practices, Action Type:        KA201: Strategic Partnership for school education)

• Inequalities and Applications

Project leader: prof. dr. sc. Josip Pečarić. Project was founded in 2014 by Croatian Science Foundation (5435)

• Various aspects of parameter estimation problem in nonlinear mathematical models

Ministry of Science, Education and Sports (2007-2013).  Project leader: prof. dr. sc. Dragan Jukić

• Statistical aspects of parameter identification problems

Ministry of Science, Education and Sports (2001-2006).  Project leader: prof. dr. sc. Mirta Benšić

Professional Activities

Editorial Board

Since 2017 member of the Editorial board of the Journal Osječki matematički list

Committee Membership 

Innovative Teaching of Matematics – National Meeting of Math Teachers, 25-26 August 2022, Osijek, Croatia

• Chair of the Organizing Committee

Innovative Teaching of Matematics – National Meeting of Math Teachers, 27-28 August 2020, Osijek, Croatia

• Member of the Programming Committee

Computational Linguistics and Golden Formula of Croatian Language – Scientific and professional conference, 22-23 May 2020, Osijek, Croatia

• Member of the Organizing Committee

Innovative Teaching of Matematics – National Meeting of Math Teachers, 30-31 August 2018, Osijek, Croatia

• Member of the Programming Committee

Innovative Teaching of Matematics – National Meeting of Math Teachers, 25-26 August 2016, Osijek, Croatia

• Member of the Organizing Committee

Refereeing/Reviewing

Journal of Mathematical Inequalities

Osječki matematički list

Service Activities

Zimska matematička škola (Winter math school) 2022-2023:

• Igrajmo se svojstvima linearne funkcije

Večer matematike 2022-2023:

• Kako pomoću linearne funkcije pobjeći iz tamnice?

Zimska matematička škola (Winter math school) 2019-2020:

• Koncept beskonačnosti

Zimska matematička škola (Winter math school) 2018-2019:

• Osnovne sredine

Festival znanosti 2016.

• Umjetnost fraktala

Zimska matematička škola (Winter math school) 2013-2014:

• Jensenova nejednakost

Teaching

Elementarna matematika

Odabrane teme iz nastave matematike

Teorija skupova

Konveksne funkcije

Integralni račun (Odjel za fiziku)

Konzultacije (Office Hours): Četvrtak (Thu) 12:00-13:00. Konzultacije su moguće i po dogovoru.