### prof. dr. sc. Mario Krnić

Redoviti profesor, Zavod za primijenjenu matematiku

Lokacija:
Telefon:
6129-965
Telefon kućni:
465
Autorske knjige

 Superadditivity and monotonicity of the Jensen-type functionals (New methods for improving the Jensen-type inequalities in real and in operator cases) . Recent Advances in Hilbert-type Inequalities . Matematička natjecanja 2008./2009 . Matematička natjecanja 2007./2008. . Matematička natjecanja 2006./2007. . Matematička natjecanja 2005./2006. . Matematička natjecanja 2004./2005. . Dirichletovo pravilo .

Udžbenici i skripta

 Matematika 3, Vektorska analiza .

Izvorni znanstveni i pregledni radovi u CC časopisima

 Improved Jensen-type inequalities via linear interpolation and applications. // Journal of Mathematical Inequalities. 11 (2017) , 2; 301-322 (članak, znanstveni). A class of Hilbert-type inequalities obtained via the improved Young inequality. // Results in mathematics. 71 (2017) , 1; 185-196 (članak, znanstveni). Multiple Hilbert-type inequalities involving some differential operators. // Banach Journal of Mathematical Analysis. 10 (2016) , 2; 320-337 (članak, znanstveni). Reverse Young-type inequalities for matrices and operators. // The Rocky Mountain journal of mathematics. 46 (2016) , 4; 1089-1105 (članak, znanstveni). More accurate Young, Heinz, and Holder inequalities for matrices. // Periodica mathematica Hungarica. 71 (2015) , 1; 78-91 (članak, znanstveni). Superadditivity of the Levinson functional and applications. // Periodica mathematica Hungarica. 71 (2015) , 2; 166-178 (članak, znanstveni). Half-discrete Hilbert-type inequalities with mean operators, the best constants, and applications. // Applied mathematics and computation. 231 (2014) ; 148-159 (članak, znanstveni). Half-discrete Hilbert-type inequalities involving differential operators. // Journal of inequalities and applications. (2014) ; 83-1-83-12 (članak, znanstveni). More precise estimates for the Jensen operator inequality obtained via the Lah-Ribarič inequality. // Applied mathematics and computation. 249 (2014) ; 346-355 (članak, znanstveni). On more accurate Hilbert-type inequalities in finite measure spaces. // Collectanea mathematica. 65 (2014) , 1; 143-154 (članak, znanstveni). More accurate weak majorization relations for the Jensen and some related inequalities. // Linear algebra and its applications. 458 (2014) ; 573-588 (članak, znanstveni). On a more accurate class of discrete Hilbert-type inequalities. // Applied mathematics and computation. 234 (2014) ; 543-547 (članak, znanstveni). On several new Hilbert-type inequalities involving means operators. // Acta mathematica sinica-english series. 29 (2013) , 8; 1493-1514 (članak, znanstveni). Refinements and reverses of means inequalities for Hilbert space operators. // Banach Journal of Mathematical Analysis. 7 (2013) , 2; 15-29 (članak, znanstveni). Refined Heinz operator inequalities. // Linear and multilinear algebra. 61 (2013) , 8; 1148-1157 (članak, znanstveni). On McShane's functional's properties and their applications. // Periodica mathematica Hungarica. 66 (2013) , 2; 159-180 (članak, znanstveni). Improved Heinz inequalities via the Jensen functional. // Central European Journal of Mathematics. 11 (2013) , 9; 1698-1710 (članak, znanstveni). A unified treatment of half-discrete Hilbert-type inequalities with a homogeneous kernel. // Mediterranean journal of mathematics. 10 (2013) , 4; 1697-1716 (članak, znanstveni). A Half-Discrete Hilbert-Type Inequality with a General Homogeneous Kernel of Degree 0. // Journal of Mathematical Inequalities. 6 (2012) , 3; 401-417 (članak, znanstveni). Superadditivity, monotonicity and exponential convexity of the Petrovic-type functionals. // Abstract and applied analysis. 2012 (2012) ; 123913-1-123913-21 (članak, znanstveni). Eigenvalue inequalities for differences of means of Hilbert space operators. // Linear algebra and its applications. 436 (2012) , 5; 1516-1527 (članak, znanstveni). Multidimensional Hilbert-type inequality on the weighted Orlicz spaces. // Mediterranean Journal of Mathematics. 9 (2012) , 4; 883-895 (članak, znanstveni). A refined discrete Hilbert inequality via the Hermite-Hadamard inequality. // Computers & mathematics with applications. 63 (2012) , 12; 1587-1596 (članak, znanstveni). Multidimensional Jensen's operator on a Hilbert space and applications. // Linear algebra and its applications. 436 (2012) , 7; 2583-2596 (članak, znanstveni). On some properties of Jensen-Mercer's functional. // Journal of Mathematical Inequalities. 6 (2012) , 1; 125-139 (članak, znanstveni). A Hilbert inequality and an Euler-Maclaurin summation formula. // Anziam Journal. 48 (2007) , Part 3; 419-431 (članak, znanstveni). Extension of Hilbert's inequality. // Journal of Mathematical Analysis and Applications. 324 (2006) , 1; 150-160 (članak, znanstveni).

 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 (članak, znanstveni). Strengthened converses of the Jensen and Edmundson-Lah-Ribarič inequalities. // Advances in Operator Theory. 1 (2016) , 1; 104-122 (članak, znanstveni). 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 (članak, znanstveni). Hilbert-type inequalities involving differential operators, the best constants, and applications. // Mathematical inequalities & applications. 18 (2015) , 1; 111-124 (članak, znanstveni). On some new converses of the Jensen and the Lah-Ribarič operator inequality. // Hacettepe Journal of Mathematics and Statistics. 44 (2015) , 5; 1045-1055 (članak, znanstveni). Weighted Montgomery identity for fractional integral of a function with respect to another function. // Georgian mathematical journal. 21 (2014) , 1; 1-10 (članak, znanstveni). On a strengthened multidimensional Hilbert-type inequality. // Mathematica slovaca. 64 (2014) , 5; 1165-1182 (članak, znanstveni). A half-discrete version of the Mulholland inequality. // Mathematical reports. 66 (2014) , 2; 163-174 (članak, znanstveni). 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 (članak, znanstveni). Hilbert-type inequalities for Hilbert space operators. // Quaestiones Methematicae. 36 (2013) , 2; 209-223 (članak, znanstveni). On some multidimensional Hilbert-type inequalities in a discrete case. // Ukrainian mathematical journal. 65 (2013) , 6; 802-813 (članak, znanstveni). Improved arithmetic-geometric and Heinz means inequalities for Hilbert space operators. // PUBLICATIONES MATHEMATICAE-DEBRECEN. 80 (2012) , 3-4; 465-478 (članak, znanstveni). On some refinements and converses of multidimensional Hilbert-type inequalities. // BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY. 85 (2012) , 3; 380-394 (članak, znanstveni). On the multidimensional Hilbert-type inequalities involving the Hardy operator. // Filomat. 26 (2012) , 4; 845-857 (članak, znanstveni). 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 (članak, znanstveni). Jessen's functional, its properties and applications. // Analele Stiintifice ale Universitatii Ovidius Constanta-Seria Matematica. 20 (2012) , 1; 225-248 (članak, znanstveni). On a multidimensional version of the Hilbert-type inequality. // Analysis Mathematica. 38 (2012) , 4; 291-303 (članak, znanstveni). On the norm of a multidimensional Hilbert-type operator. // Sarajevo journal of mathematics. 7 (2011) , 2; 223-243 (članak, znanstveni). General Hardy-type inequalities with non-onjugate exponents. // Bulletin of the Iranian Mathematical Society. 37 (2011) , 3; 77-108 (članak, znanstveni). On Some Properties of Jensen-Steffensen's Functional. // Annals of the University of Craiova-Mathematics and Computer Science Series. 38 (2011) , 2; 43-54 (članak, znanstveni). Discrete Hilbert-type inequalities with general homogeneous kernels. // Rendiconti del Circolo Matematico di Palermo. 60 (2011) , 1-2; 161-171 (članak, znanstveni). Hilbert-type inequalities and related operators with homogeneous kernel of degree 0. // Mathematical inequalities & applications. 13 (2010) , 4; 817-839 (članak, znanstveni). Hilbert inequality and Gaussian hypergeometric functions. // Journal of mathematical inequalities. 3 (2009) , 4; 645-656 (članak, znanstveni). 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 (članak, znanstveni). General Hilbert-Type Inequalities with Non-conjugate Exponents. // Mathematical inequalities & applications. 11 (2008) , 2; 237-269 (članak, znanstveni). On some higher-dimensional Hilbert's and Hardy-Hilbert's integral inequalities with parameters. // Mathematical inequalities & applications. 11 (2008) , 4; 701-716 (članak, znanstveni). Hilbert Inequalities Related to Generalized Hypergeometric Functions mFn. // Mathematica balkanica. 22 (2008) , 3-4; 307-322 (članak, znanstveni). Some improvements on general Hilbert inequality. // Nonlinear Functional Analysis and Applications. 12 (2007) , 1; 21-40 (članak, znanstveni). On some general Hilbert's Inequalities with non-conjugate parameters. // Rendiconti del Circolo Matematico di Palermo. II (2007) , LVI; 219-234 (članak, znanstveni). Some remarks on reverse Hilbert and Hardy-Hilbert type inequalities. // Rendiconti del Circolo Matematico di Palermo. II (2007) , LVI; 349-357 (članak, znanstveni). Generalization of Hilbert's and Hardy-Hilbert's Integral Inequality. // Mathematical Inequalities and Applications. 8 (2005.) , 2; 259-272 (članak, znanstveni). Multiple Hilbert and Hardy-Hilbert inequalities with non-conjugate parameters. // Bulletin of the Australian Mathematical Society. 71 (2005) ; 447-457 (članak, znanstveni). On the Best Constant in Hilbert's Inequality. // Mathematical Inequalities and Applications. 8 (2005.) , 2; 317-329 (članak, znanstveni). Hilbert's inequalities and their reverses. // Publicationes Mathematicae Debrecen. 67 (2005.) , 3-4; 315-331 (članak, znanstveni). General Hilbert's and Hardy's inequalities. // Mathematical inequalities & applications. 8 (2005) , 1; 29-51 (članak, znanstveni).

 More accurate Jensen-type inequalities for signed measures characterized via Green function and applications. // Turkish Journal of Mathematics. (2017) (prihvaćen za objavljivanje).

Plenarna izlaganja

 Superadditivity of the Jensen-type functionals and applications // Mathematical Inequalities and Applications, MIA 2014.

Sažeci u zbornicima skupova

 Yet another method for bounding Jensen's functional for the operators on a Hilbert space // . Superadditivity of the Levinson functional and applications // . Improved variants of Young, Heinz and Hölder inequalities for matrices // . More precise weak majorization relations for the Jensen inequality and applications // 5th Congress of Mathematicians of Macedonia. On the eigenvalue inequalities for differences of means of Hilbert space operators // . Jensen-type functionals for the operators on a Hilbert space // . On Some Improvements of Hoelder's Inequality // 2nd International Eurasian Conference on Mathematical Sciences and Applications, Abstracts book. 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.. Multidimensional Hilbert-type inequality on the weighted Orlicz spaces // Book of Abstracts -- 5th Croatian Mathematical Congress. 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. 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. Extension of Hilbert's Inequality // Fourth Croatian Mathematical Congress, Osijek, Croatia. Hilbert inequality and Gaussian hypergeometric functions // Mathematical Inequalities and Applications, Trogir, Croatia. General Hilbert's and Hardy-Hilbert's Inequality // Treći hrvatski matematički kongres / Nikica Uglešić (ur.). General Hilbert's inequalities with non-conjugate parameters // Third Croatian Congress of Mathematics.

Disertacije

 O nekim nejednakostima Hilbertovog tipa / doktorska disertacija.

 Reprezentacije grupa pletenica i kvantne grupe / magistarski rad.

Vođenje disertacija, magistarskih i diplomskih radova

 Superaditivnost funkcionala Jensenovog tipa i primjene / doktorska disertacija. Poopćenja i profinjenja Jensen-Steffensenove i njoj srodnih nejednakosti / doktorska disertacija.