prof. dr. sc. Mario Krnić

Full professor, Department of Applied Mathematics

Location:
Public phone number:
6129-965
Internal phone number:
465
  Author's books
 

1. Krnić, Mario; Lovričević, Neda; Pečarić, Josip; Perić, Jurica.
Superadditivity and monotonicity of the Jensen-type functionals (New methods for improving the Jensen-type inequalities in real and in operator cases) .
Zagreb : Element, 2015 (monograph).

2. Krnić, Mario; Pečarić, Josip; Perić, Ivan; Vuković, Predrag.
Recent Advances in Hilbert-type Inequalities .
Zagreb : Element, 2012 (monograph).

3. Hanjš, Željko; Krnić, Mario.
Mathematical Competitions 2008./2009. .
Zagreb : Element d.o.o., 2010 (proceedings).

4. Hanjš, Željko; Krnić, Mario.
Mathematical Competitions 2007/2008 .
Zagreb : Element d.o.o.,, 2009. (proceedings).

5. Hanjš, Željko; Krnić, Mario.
Mathematical Competitions 2006/2007 .
Zagreb : Element i Hrvatsko matematičko društvo, 2008. (proceedings).

6. Balagović, Martina; Hanjš, Željko; Krnić, Mario.
Mathematics competitions 2005/2006 .
Zagreb : Element, 2007 (proceedings).

7. Hanjš, Željko; Kovač, Vjekoslav; Krnić, Mario.
Mathematical Competitions 2004/2005 .
Zagreb : Element, Zagreb ; Hrvatsko matematičko društvo, 2006 (proceedings).

8. Krnić, Mario.
The pigenhole principle .
Zagreb : Hrvatsko matematičko društvo, 2001 (handbook).
 
  Textbooks and scripts
 

1. Burić, Tomislav; Korkut, Luka; Krnić, Mario; Milišić, Josipa Pina; Pašić, Mervan.
Mathematics 3, Vector analysis .
Zagreb : Element, 2010.
 
  Journal articles and review articles in CC journals
 

1. Choi, Daeshik; Krnić, Mario; Pečarić, Josip.
Improved Jensen-type inequalities via linear interpolation and applications. // Journal of Mathematical Inequalities. 11 (2017) , 2; 301-322 (journal article).

2. Krnić, Mario; Vuković, Predrag.
A class of Hilbert-type inequalities obtained via the improved Young inequality. // Results in mathematics. 71 (2017) , 1; 185-196 (journal article).

3. Adiyasuren, Vandanjav; Batbold, Tserendorj; Krnić, Mario.
Multiple Hilbert-type inequalities involving some differential operators. // Banach Journal of Mathematical Analysis. 10 (2016) , 2; 320-337 (journal article).

4. Bakherad, Mojtaba; Krnić, Mario; Moslehian, Mohammad Sal.
Reverse Young-type inequalities for matrices and operatorss. // The Rocky Mountain journal of mathematics. 46 (2016) , 4; 1089-1105 (journal article).

5. Krnić, Mario.
More accurate Young, Heinz, and Holder inequalities for matrices. // Periodica mathematica Hungarica. 71 (2015) , 1; 78-91 (journal article).

6. Krnić, Mario; Lovričević, Neda; Pečarić, Josip.
Superadditivity of the Levinson functional and applications. // Periodica mathematica Hungarica. 71 (2015) , 2; 166-178 (journal article).

7. Adiyasuren, Vandanjav; Batbold, Tserendorj; Krnić, Mario.
Half-discrete Hilbert-type inequalities with mean operators, the best constants, and applications. // Applied mathematics and computation. 231 (2014) ; 148-159 (journal article).

8. Adiyasuren, Vandanjav; Batbold, Tserendorj; Krnić, Mario.
Half-discrete Hilbert-type inequalities involving differential operators. // Journal of inequalities and applications. (2014) ; 83-1-83-12 (journal article).

9. Jakšić, Rozarija; Krnić, Mario; Pečarić, Josip.
More precise estimates for the Jensen operator inequality obtained via the Lah-Ribarič inequality. // Applied mathematics and computation. 249 (2014) ; 346-355 (journal article).

10. Krnić, Mario; Pečarić, Josip.
On more accurate Hilbert-type inequalities in finite measure spaces. // Collectanea mathematica. 65 (2014) , 1; 143-154 (journal article).

11. Krnić, Mario; Pečarić, Josip.
More accurate weak majorization relations for the Jensen and some related inequalities. // Linear algebra and its applications. 458 (2014) ; 573-588 (journal article).

12. Krnić, Mario; Vuković, Predrag.
On a more accurate class of discrete Hilbert-type inequalities. // Applied mathematics and computation. 234 (2014) ; 543-547 (journal article).

13. Adiyasuren, Vandanjav; Batbold, Tserendorj; Krnić, Mario.
On several new Hilbert-type inequalities involving means operators. // Acta mathematica sinica-english series. 29 (2013) , 8; 1493-1514 (journal article).

14. Hirzallah, Omar; Kittaneh, Fuad; Krnić, Mario; Lovričević, Neda; Pečarić, Josip.
Refinements and reverses of means inequalities for Hilbert space operators. // Banach Journal of Mathematical Analysis. 7 (2013) , 2; 15-29 (journal article).

15. Kittaneh, Fuad; Krnić, Mario.
Refined Heinz operator inequalities. // Linear and multilinear algebra. 61 (2013) , 8; 1148-1157 (journal article).

16. Krnić, Mario; Lovričević, Neda; Pečarić, Josip.
On McShane's functional's properties and their applications. // Periodica mathematica Hungarica. 66 (2013) , 2; 159-180 (journal article).

17. Krnić, Mario; Pečarić, Josip.
Improved Heinz inequalities via the Jensen functional. // Central European Journal of Mathematics. 11 (2013) , 9; 1698-1710 (journal article).

18. Krnić, Mario; Pečarić, Josip; Vuković, Predrag.
A unified treatment of half-discrete Hilbert-type inequalities with a homogeneous kernel. // Mediterranean journal of mathematics. 10 (2013) , 4; 1697-1716 (journal article).

19. Bicheng, Yang; Krnić, Mario.
A Half-Discrete Hilbert-Type Inequality with a General Homogeneous Kernel of Degree 0. // Journal of Mathematical Inequalities. 6 (2012) , 3; 401-417 (journal article).

20. Butt, Saad Ihsan; Krnić, Mario; Pečarić, Josip.
Superadditivity, monotonicity and exponential convexity of the Petrovic-type functionals. // Abstract and applied analysis. 2012 (2012) ; 123913-1-123913-21 (journal article).

21. Hirzzalah, Omar; Kittaneh, Fuad; Krnić, Mario; Lovričević, Neda; Pečarić, Josip.
Eigenvalue inequalities for differences of means of Hilbert space operators. // Linear algebra and its applications. 436 (2012) , 5; 1516-1527 (journal article).

22. Krnić, Mario.
Multidimensional Hilbert-type inequality on the weighted Orlicz spaces. // Mediterranean Journal of Mathematics. 9 (2012) , 4; 883-895 (journal article).

23. Krnić, Mario.
A refined discrete Hilbert inequality via the Hermite-Hadamard inequality. // Computers & mathematics with applications. 63 (2012) , 12; 1587-1596 (journal article).

24. Krnić, Mario; Lovričević, Neda; Pečarić, Josip.
Multidimensional Jensen's operator on a Hilbert space and applications. // Linear algebra and its applications. 436 (2012) , 7; 2583-2596 (journal article).

25. Krnić, Mario; Lovričević, Neda; Pečarić, Josip.
On some properties of Jensen-Mercer's functional. // Journal of Mathematical Inequalities. 6 (2012) , 1; 125-139 (journal article).

26. Krnić, Mario; Pečarić, Josip.
A Hilbert inequality and an Euler-Maclaurin summation formula. // Anziam Journal. 48 (2007) , Part 3; 419-431 (journal article).

27. Krnić, Mario; Pečarić Josip.
Extension of Hilbert's inequality. // Journal of Mathematical Analysis and Applications. 324 (2006) , 1; 150-160 (journal article).
 
  Scientific papers in other journals
 

1. Choi, Daeshik; Krnić, Mario; Pečarić, Josip.
More accurate classes of Jensen-type inequalities for convex and operator convex functions. // Mathematical Inequalities & Applications. 21 (2018) , 2; 301-321 (journal article).

2. Jakšić, Rozarija; Krnić, Mario; Pečarić, Josip.
More accurate converses of the Jensen and the Lah-Ribarič operator inequality. // Annals of the Alexandru Ioan Cuza University - Mathematics. LXII (2016) , 2; 553-562 (journal article).

3. Krnić, Mario; Mikić, Rozarija; Pečarić, Josip.
Strengthened converses of the Jensen and Edmundson-Lah-Ribarič inequalities. // Advances in Operator Theory. 1 (2016) , 1; 104-122 (journal article).

4. Adiyasuren, Vandanjav; Batbold, Tserendorj; Krnić, Mario.
The best constants in multidimensional Hilbert-type inequalities involving some weighted means operators. // Bulletin of the Malaysian Mathematical Sciences Society. 38 (2015) , 3; 1001-1022 (journal article).

5. Adiyasuren, Vandanjav; Batbold, Tserendorj; Krnić, Mario.
Hilbert-type inequalities involving differential operators, the best constants, and applications. // Mathematical inequalities & applications. 18 (2015) , 1; 111-124 (journal article).

6. Jakšić, Rozarija; Krnić, Mario; Pečarić, Josip.
On some new converses of the Jensen and the Lah-Ribarič operator inequality. // Hacettepe Journal of Mathematics and Statistics. 44 (2015) , 5; 1045-1055 (journal article).

7. Aglić Aljinović, Andrea; Krnić, Mario; Pečarić, Josip.
Weighted Montgomery identity for fractional integral of a function with respect to another function. // Georgian mathematical journal. 21 (2014) , 1; 1-10 (journal article).

8. Krnić, Mario.
On a strengthened multidimensional Hilbert-type inequality. // Mathematica slovaca. 64 (2014) , 5; 1165-1182 (journal article).

9. Yang, Bicheng; Krnić, Mario.
A half-discrete version of the Mulholland inequality. // Mathematical reports. 66 (2014) , 2; 163-174 (journal article).

10. Čižmešija, Aleksandra; Krnić, Mario.
A strengthened form of a general Hardy-type inequality obtained via superquadraticity and its applications. // International journal of pure and applied mathematics. 86 (2013) , 2; 257-282 (journal article).

11. Krnić, Mario.
Hilbert-type inequalities for Hilbert space operators. // Quaestiones Methematicae. 36 (2013) , 2; 209-223 (journal article).

12. Krnić, Mario; Vuković, Predrag.
On some multidimensional Hilbert-type inequalities in a discrete case. // Ukrainian mathematical journal. 65 (2013) , 6; 802-813 (journal article).

13. Kittaneh, Fuad; Krnić, Mario; Lovričević, Neda; Pečarić, Josip.
Improved arithmetic-geometric and Heinz means inequalities for Hilbert space operators. // PUBLICATIONES MATHEMATICAE-DEBRECEN. 80 (2012) , 3-4; 465-478 (journal article).

14. Krnić, Mario.
On some refinements and converses of multidimensional Hilbert-type inequalities. // BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY. 85 (2012) , 3; 380-394 (journal article).

15. Krnić, Mario.
On the multidimensional Hilbert-type inequalities involving the Hardy operator. // Filomat. 26 (2012) , 4; 845-857 (journal article).

16. Krnić, Mario; Lovričević, Neda; Pečarić, Josip.
Jensen's Operator and Applications to Mean Inequalities for Operators in Hilbert Space. // Bulletin of the Malaysian Mathematical Sciences Society. 35 (2012) , 1; 1-14 (journal article).

17. Krnić, Mario; Lovričević, Neda; Pečarić, Josip.
Jessen's functional, its properties and applications. // Analele Stiintifice ale Universitatii Ovidius Constanta-Seria Matematica. 20 (2012) , 1; 225-248 (journal article).

18. Krnić, Mario; Vuković, Predrag.
On a multidimensional version of the Hilbert-type inequality. // Analysis Mathematica. 38 (2012) , 4; 291-303 (journal article).

19. Bicheng, Yang; Krnić, Mario.
On the norm of a multidimensional Hilbert-type operator. // Sarajevo journal of mathematics. 7 (2011) , 2; 223-243 (journal article).

20. Čižmešija, Aleksandra; Krnić, Mario; Pečarić, Josip.
General Hardy-type inequalities with non-onjugate exponents. // Bulletin of the Iranian Mathematical Society. 37 (2011) , 3; 77-108 (journal article).

21. Krnić, Mario; Lovričević, Neda; Pečarić, Josip.
On Some Properties of Jensen-Steffensen's Functional. // Annals of the University of Craiova-Mathematics and Computer Science Series. 38 (2011) , 2; 43-54 (journal article).

22. Krnić, Mario; Pečarić, Josip; Vuković, Predrag.
Discrete Hilbert-type inequalities with general homogeneous kernels. // Rendiconti del Circolo Matematico di Palermo. 60 (2011) , 1-2; 161-171 (journal article).

23. Bicheng Yang; Krnić, Mario.
Hilbert-type inequalities and related operators with homogeneous kernel of degree 0. // Mathematical inequalities & applications. 13 (2010) , 4; 817-839 (journal article).

24. Krnić, Mario.
Hilbert inequality and Gaussian hypergeometric functions. // Journal of mathematical inequalities. 3 (2009) , 4; 645-656 (journal article).

25. Krnić, Mario; Pečarić, Josip; Perić, Ivan; Vuković, Predrag.
Hardy-Hilbert type inequalities with fractional kernel in ${; ; ; \bf R}; ; ; ^n$. // Journal of inequalities in pure and applied mathematics. 10 (2009) , 4; 115-1-115-19 (journal article).

26. Čižmešija, Aleksandra; Krnić, Mario; Pečarić, Josip.
General Hilbert-Type Inequalities with Non-conjugate Exponents. // Mathematical inequalities & applications. 11 (2008) , 2; 237-269 (journal article).

27. Krnić, Mario; Pečarić, Josip; Vuković, Predrag.
On some higher-dimensional Hilbert's and Hardy-Hilbert's integral inequalities with parameters. // Mathematical inequalities & applications. 11 (2008) , 4; 701-716 (journal article).

28. Krnić, Mario; Tomovski Živorad; Pečarić Josip.
Hilbert Inequalities Related to Generalized Hypergeometric Functions mFn. // Mathematica balkanica. 22 (2008) , 3-4; 307-322 (journal article).

29. Krnić, Mario; Pečarić Josip.
Some improvements on general Hilbert inequality. // Nonlinear Functional Analysis and Applications. 12 (2007) , 1; 21-40 (journal article).

30. Krnić, Mario; Pečarić, Josip.
On some general Hilbert's Inequalities with non-conjugate parameters. // Rendiconti del Circolo Matematico di Palermo. II (2007) , LVI; 219-234 (journal article).

31. Krnić, Mario; Pečarić, Josip; Vuković Predrag.
Some remarks on reverse Hilbert and Hardy-Hilbert type inequalities. // Rendiconti del Circolo Matematico di Palermo. II (2007) , LVI; 349-357 (journal article).

32. Bicheng, Yang; Brnetić, Ilko; Krnić, Mario; Pečarić, Josip.
Generalization of Hilbert's and Hardy-Hilbert's Integral Inequality. // Mathematical Inequalities and Applications. 8 (2005.) , 2; 259-272 (journal article).

33. Brnetić, Ilko; Krnić, Mario; Pečarić, Josip.
Multiple Hilbert and Hardy-Hilbert inequalities with non-conjugate parameters. // Bulletin of the Australian Mathematical Society. 71 (2005) ; 447-457 (journal article).

34. Krnić, Mario; Mingzhe, Gao; Pečarić, Josip; Xuemei, Gao.
On the Best Constant in Hilbert's Inequality. // Mathematical Inequalities and Applications. 8 (2005.) , 2; 317-329 (journal article).

35. Krnić, Mario; Pečarić, Josip.
Hilbert's inequalities and their reverses. // Publicationes Mathematicae Debrecen. 67 (2005.) , 3-4; 315-331 (journal article).

36. Krnić, Mario; Pečarić, Josip.
General Hilbert's and Hardy's inequalities. // Mathematical inequalities & applications. 8 (2005) , 1; 29-51 (journal article).
 
  Papers in the publishing process
 

1. Krnić, Mario; Pečarić, Josip; Rodić, Mirna.
More accurate Jensen-type inequalities for signed measures characterized via Green function and applications. // Turkish Journal of Mathematics. (2017) (accepted for publication).
 
  Plenary/Keynote talks
 

1. Krnić, Mario.
Superadditivity of the Jensen-type functionals and applications // Mathematical Inequalities and Applications, MIA 2014.
(plenary/keynote lecture,international peer-review,abstract,scientific).
 
  Abstracts in Book of abstracts
 

1. Krnić, Mario; Lovričević, Neda; Pečarić, Josip.
Yet another method for bounding Jensen's functional for the operators on a Hilbert space // .
(lecture,international peer-review,abstract,scientific).

2. Krnić, Mario; Lovričević, Neda; Pečarić, Josip.
Superadditivity of the Levinson functional and applications // .
(lecture,international peer-review,abstract).

3. Mario Krnić.
Improved variants of Young, Heinz and Hölder inequalities for matrices // .
(lecture,international peer-review,abstract,scientific).

4. Krnić, Mario; Pečarić, Josip.
More precise weak majorization relations for the Jensen inequality and applications // 5th Congress of Mathematicians of Macedonia.
(lecture,international peer-review,abstract).

5. Hirzallah, Omar; Kittaneh, Fuad; Krnić, Mario; Lovričević, Neda; Pečarić, Josip.
On the eigenvalue inequalities for differences of means of Hilbert space operators // .
(poster,international peer-review,abstract,scientific).

6. Lovričević, Neda; Kittaneh, Fuad; Krnić, Mario; Pečarić, Josip.
Jensen-type functionals for the operators on a Hilbert space // .
(lecture,international peer-review,abstract,scientific).

7. Lovričević, Neda; Krnić, Mario; Pečarić, Josip.
On Some Improvements of Hoelder's Inequality // 2nd International Eurasian Conference on Mathematical Sciences and Applications, Abstracts book.
Sarajevo, 2013. 109-109 (lecture,international peer-review,abstract,scientific).

8. Krnić, Mario; Lovričević, Neda; Pečarić, Josip.
Superadditivity of some Jensen-type functionals // Book of abstracts - 5th Croatian Mathematical Congress, 18-21 June, 2012, Rijeka, Croatia / Crnković, Dean ; Mikulić Crnković, Vedrana ; Rukavina, Sanja (ur.). Rijeka: Department of Mathematics, University of Rijeka, 2012..
62-62 (lecture,international peer-review,abstract,scientific).

9. Mario Krnić.
Multidimensional Hilbert-type inequality on the weighted Orlicz spaces // Book of Abstracts -- 5th Croatian Mathematical Congress.
61-61 (lecture,international peer-review,abstract,scientific).

10. Krnić, Mario.
Hilbert inequalities related to generalized hypergeometric functions // Analysis, Inequalities and Homogenization Theory (AIHT)– midnightsun conference in honour of Professor Lars-Erik Persson on the occasion of his 65th birthday, Lulea, Sweden.
(lecture,international peer-review,abstract,scientific).

11. Krnić, Mario; Pečarić Josip; Vuković Predrag.
On some higher-dimensional Hilbert's and Hardy-Hilbert's integral inequalities with parameters // Mathematical Conference, 85 Years of Professor Blagoj Popov Life, Ohrid, Macedonia.
(lecture,international peer-review,abstract,scientific).

12. Krnić, Mario; Pečarić, Josip.
Extension of Hilbert's Inequality // Fourth Croatian Mathematical Congress, Osijek, Croatia.
(poster,international peer-review,abstract,scientific).

13. Krnić, Mario.
Hilbert inequality and Gaussian hypergeometric functions // Mathematical Inequalities and Applications, Trogir, Croatia.
(lecture,international peer-review,abstract,scientific).

14. Brnetić, Ilko; Krnić, Mario; Pečarić, Josip.
General Hilbert's and Hardy-Hilbert's Inequality // Treći hrvatski matematički kongres / Nikica Uglešić, editor(s).
Split : Hrvatsko matematičko društvo, 2004. 26-26 (lecture,abstract,scientific).

15. Čižmešija, Aleksandra; Krnić, Mario; Pečarić, Josip.
General Hilbert's inequalities with non-conjugate parameters // Third Croatian Congress of Mathematics.
2004. (abstract,scientific).
 
  Dissertations
 

1. Krnić, Mario.
On some inequalities of Hilbert's type / doctoral thesis.
Zagreb : Prirodoslovno-matematički fakultet, Matematički odjel, 27.10. 2004, 130 pages. Mentor: Pečarić, Josip.
 
  Master thesis
 

1. Krnić, Mario.
Representations of braid groups and quantum groups / pre-Bologna master thesis.
Zagreb : Prirodoslovno-matematički fakultet, Matematički odjel, 20.12. 2000, 153 pages. Mentor: Svrtan, Dragutin.
 
  Mentoring
 

1. Lovričević, Neda.
Superadditivity of the Jensen-type functionals and applications / doctoral thesis.
Zagreb : PMF - Matematički odsjek, 09.07. 2012., 134 pages. Mentor: Krnić, Mario.

2. Ivelić, Slavica.
Generalizations and refinements of the Jensen-Steffensen and its associated inequalities / doctoral thesis.
Zagreb : Prirodoslovno matematički fakultet - Matematički odsjek, 26.07. 2011, 126 pages. Mentor: Matković, Anita.
 

Teaching duties

Post-graduation study

University undergraduate

University graduate