Head of the research group

Group members

  • Full Prof. Marko Matić, PhD
  • Full Prof. Josip Pečarić, PhD,  akademik, Tekstilno-tehnološki fakultet Sveučilišta u Zagrebu

Deparmtnet of Mathematics

Research areas:

Mathematical inequalities and their applications in numerical analysis, generalizations of convexity and applications

Research description:

We will try to establish some new methods for improvement of the classical inequalities for convex functions, such as the Hermite-Hadamard inequalities, Jensen’s inequality and the converse Jensen inequality. As special cases of those improvements we can obtain refinements of the converse Holder inequality and the converse Minkowski inequality. The obtained improvements and of the Jensen inequality and its converse can be used to establish new inequalities related to the Shannon entropy and the Zipf-Mandelbrot law both of which have considerable importance in Information theory. We also investigate various classes of generalized convex functions as well as some classes of functions which produce sharper variants of the classical inequalities for convex functions, for instance superquadratic functions and strongly convex functions. We will try to establish certain integral inequalities which will enable us to obtain better bounds for the reminder of some corrected quadrature formulae.

Contacts with academic and other institutions:

1. Prirodoslovno-matematički fakultet Sveučilišta u Zagrebu
2. Tekstilno-tehnološki fakultet Sveučilišta u Zagrebu
3. Fakultet strojarstva i brodogradnje Sveučilišta u Zagrebu
4. Matematički odjel Sveučilišta u Osijeku
5. Department of Mathematics, University of Bielsko-Biala, Poland
6. Department of Mathematics, University of Debrecen, Hungary
7. Department of Mathematics, University of Haifa, Israel

Description of the current cooperation:

Current cooperation is mainly conducted trough joint research which is visible in the considerable number of joint papers, but beside that it is also carried out trough participation in various international conferences and symposiums organized by our research groups in Croatia, Poland and Hungary and in joint seminars via ERASMUS+ mobility.

Plans for future research:

We will continue with the previously mentioned research.

List of selected research papers:

1. Klaričić Bakula, Milica; Nikodem, Kazimierz. On the converse Jensen inequality for strongly convex functions. Journal of mathematical analysis and applications. 434 (2016) , 1; 516-522.
2. Banić, Senka; Klaričić Bakula, Milica. Jensen’s inequality for functions superquadratic on the coordinates. Journal of Mathematical Inequalities. 9 (2015) , 4; 1365-1375.
3. Klaričić Bakula, Milica; Pečarić, Josip; Ribičić Penava, Mihaela; Vukelić, Ana. New estimations of the remainder in three-point quadrature formulae of Euler type. Journal of Mathematical Inequalities. 9 (2015) , 4; 1143-1156.
4. Klaričić Bakula, Milica; Pečarić, Josip; Ribičić Penava, Mihaela; Vukelić, Ana. Some Grüss type inequalities and corrected three-point quadrature formulae of Euler type. Journal of inequalities and applications. (2015) ; 76-1-76-14.
5. Bibi, Rabia; Pečarić, Josip; Perić, Jurica. Improvements of the Hermite–Hadamard inequality on time scales. Journal of mathematical inequalities. 9 (2015) , 3; 913-934.
6. Matković, Anita; Pečarić, Josip; Perić, Jurica. A refinement of the Jessen-Mercer inequality and a generalization on convex hulls in R^k. Journal of Mathematical Inequalities. 9 (2015) , 4; 1093-1114.
7. Klaričić Bakula, Milica. An improvement of the Hermite-Hadamard inequality for functions convex on the coordinates. The Australian journal of mathematical analysis and applications. 11 (2014) , 1; 1-7.
8. Klaričić Bakula, Milica; Pečarić, Josip; Ribičić Penava, Mihaela; Vukelić, Ana. Some inequalities for the Čebyšev functional and general four-point quadrature formulae of Euler type. Matematički bilten. 38 (2014) , 2; 69-80.
9. Klaričić Bakula, Milica; Pečarić, Josip; Ribičić Penava, Mihaela. General quadrature formulae based on the weighted Montgomery identity and related inequalities. Rad Hrvatske akademije znanosti i umjetnosti. Razred za matematičke, fizičke i kemijske znanosti. Matematičke znanosti. 17 (2013) ; 139-150.
10. Mićić, Jadranka; Pečarić Josip; Perić, Jurica. Refined converses of Jensen’s operator inequality. Journal of inequalities and applications. (2013) , 353; 1-16.
11. Mićić, Jadranka; Pečarić, Josip; Perić, Jurica. Refined Jensen’s operator inequality with condition on spectra. Operators and matrices. 7 (2013) , 2; 293-308.
12. Pečarić, Josip; Perić, Jurica. Generalizations and improvements of converse Jensen’s inequality for convex hulls in R^k. Mathematical inequalities and applications. 17 (2013) ; 1125-1137.
13. Mićić, Jadranka; Pečarić, Josip; Perić, Jurica. Extension of the refined Jensen’s operator inequality with condition on spectra. Annals of Functional Analysis. 3 (2012) , 1; 67-85.
14. Klaričić Bakula, Milica; Pečarić, Josip; Perić, Jurica. Extensions of the Hermite-Hadamard inequality with applications. Mathematical inequalities and applications. 15 (2012) , 4; 899-921.
15. Pečarić, Josip; Perić, Jurica. Remarks on the paper “Jensen’s inequality and new entropy bounds” of S. Simić. Journal of mathematical inequalities. 6 (2012) , 4; 631-636.
16. Klaričić Bakula, Milica; Pečarić, Josip; Perić, Jurica. On the converse Jensen inequality. Applied mathematics and computation. 218 (2012) , 11; 6566-6575.
17. Ivelić, Slavica; Klaričić Bakula, Milica; Pečarić, Josip. Converse Jensen-Steffensen inequality. Aequationes mathematicae. 82 (2011) , 3; 233-246.
18. Klaričić Bakula, Milica; Matić, Marko; Pečarić, Josip. Generalizations of the Jensen-Steffensen and related inequalities. Central European Journal of Mathematics. 7 (2009) , 4; 787-803.
19. Klaričić Bakula, Milica; Ribičić Penava, Mihaela. General four-point quadrature formulae with applications for α-L-Hölder type functions. Journal of mathematical ineqalities. 3 (2009) , 3; 427-436.
20. Kirmaci, U.S.; Klaričić Bakula, Milica; Özdemir, M.E.; Pečarić, Josip. Hadamard-type inequalities for s-convex functions. Applied Mathematics and Computation. 193 (2007) , 1; 26-35.

Start typing and press Enter to search

Skip to content