Mario Krnić - Academia.edu (original) (raw)

Papers by Mario Krnić

Research paper thumbnail of Jessen's functional, its properties and applications

Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2012

In this paper we consider Jessen's functional, defined by means of a positive isotonic linear fun... more In this paper we consider Jessen's functional, defined by means of a positive isotonic linear functional, and investigate its properties. Derived results are then applied to weighted generalized power means, which yields extensions of some recent results, known from the literature. In particular, we obtain the whole series of refinements and converses of numerous classical inequalities such as the arithmetic-geometric mean inequality, Young's inequality and Hölder's inequality.

Research paper thumbnail of Obituary

Research paper thumbnail of Recent advances in Hilbert-type inequalities. A unified treatment of Hilbert-type inequalities

Research paper thumbnail of Some remarks on reverse Hilbert and Hardy-Hilbert type inequalities

Rendiconti del Circolo Matematico di Palermo, 2007

In this paper we obtain an extension of discrete Hilbert's inequality, by using some numerical me... more In this paper we obtain an extension of discrete Hilbert's inequality, by using some numerical methods. We shall obtain, in a similar way as Yang did in , that the parameter from the kernel can be taken from the interval [3/2, 3). We also compare our findings with existing results, known from the literature.

Research paper thumbnail of On some general Hilbert’s inequalities with non-conjugate parameters

Rendiconti del Circolo Matematico di Palermo, 2007

A generalized discrete Hilbert’s and Hardy-Hilbert’s inequality with non-conjugate parameters can... more A generalized discrete Hilbert’s and Hardy-Hilbert’s inequality with non-conjugate parameters can be established by means of Euler-Maclaurin summation formula. We derive some general results for homogeneous functions and compare our results with some previously known from the literature. We also obtain the improvements on some earlier results.

Research paper thumbnail of Discrete Hilbert-type inequalities with general homogeneous kernels

Rendiconti del Circolo Matematico di Palermo, 2011

The main objective of this paper is an unified treatment of discrete Hilbert-type inequalities wi... more The main objective of this paper is an unified treatment of discrete Hilbert-type inequalities with homogeneous kernels. At the beginning, we prove and discuss two equivalent general inequalities of such type. Further, we analyze the conditions which yield the best possible constant factors in obtained inequalities. The obtained results are then applied to various settings considering homogeneous functions of a

Research paper thumbnail of Multidimensional Jensen’s operator on a Hilbert space and applications

Linear Algebra and its Applications, 2012

Motivated by a joint concavity of connections, solidarities and multidimensional weighted geometr... more Motivated by a joint concavity of connections, solidarities and multidimensional weighted geometric mean, in this paper we extend an idea of convexity (concavity) to operator functions of several variables. With the help of established definitions, we introduce the so called multidimensional Jensen's operator and study its properties. In such a way we get the lower and upper bounds for the above mentioned operator, expressed in terms of non-weighted operator of the same type. As an application, we obtain both refinements and converses for operator variants of some well-known classical inequalities. In order to obtain the refinement of Jensen's integral inequality, we also consider an integral analogue of Jensen's operator for functions of one variable.

Research paper thumbnail of Extension of Hilbert's inequality

Journal of Mathematical Analysis and Applications, 2006

In this paper we make some further extensions of discrete Hilbert's inequality by using Euler-Mac... more In this paper we make some further extensions of discrete Hilbert's inequality by using Euler-Maclaurin summation formula. We give the improvements of some previously obtained results and also compare our results with some previously known from the literature.

Research paper thumbnail of Refinements and reverses of means inequalities for Hilbert space operators

Banach Journal of Mathematical Analysis, 2013

In this paper we derive some improvements of means inequalities for Hilbert space operators. More... more In this paper we derive some improvements of means inequalities for Hilbert space operators. More precisely, we obtain refinements and reverses of the arithmetic-geometric operator mean inequality. As an application, we also deduce an improved variant for the refined arithmetic-Heinz mean inequality. We also present some eigenvalue inequalities for differences of certain operator means.

Research paper thumbnail of A Unified Treatment of Half-Discrete Hilbert-Type Inequalities with a Homogeneous Kernel

Mediterranean Journal of Mathematics, 2013

ABSTRACT In this paper we provide a unified treatment of half-discrete Hilbert-type inequalities ... more ABSTRACT In this paper we provide a unified treatment of half-discrete Hilbert-type inequalities with a general homogeneous kernel. The main results are proved for the case of non-conjugate exponents. A special emphasis is given to determining conditions under which these inequalities include the best possible constants. As an application, we consider some operator expressions closely connected to established inequalities. Finally, we also provide improvements of derived half-discrete inequalities by virtue of the Hermite-Hadamard inequality.

Research paper thumbnail of On some higher-dimensional Hilbert's and Hardy-Hilbert's integral inequalities with parameters

Mathematical Inequalities & Applications, 2008

ABSTRACT A higher dimensional Hilbert’s inequality and a higher dimensional Hardy-Hilbert’s inequ... more ABSTRACT A higher dimensional Hilbert’s inequality and a higher dimensional Hardy-Hilbert’s inequality in non-conjugate case are established. It is also shown that in the conjugate case, the constants in the inequalities are best possible under some appropriate conditions.

Research paper thumbnail of General Hilbert-type inequalities with non-conjugate exponents

Mathematical Inequalities & Applications, 2008

ABSTRACT

Research paper thumbnail of GENERALIZATION OF HILBERT AND HARDY–HILBERT INTEGRAL INEQUALITIES

Abstract. The main objective of this paper is a study of some new generalizations of Hilbert’s an... more Abstract. The main objective of this paper is a study of some new generalizations of Hilbert’s and Hardy-Hilbert’s type inequalities. We establish general form of multiple Hilbert-type inequality and we also introduce multiple inequality of Hardy-Hilbert type. Further, the best possible constants are obtained for some general cases. Mathematics subject classification (2000): 26D15.

Research paper thumbnail of Eigenvalue inequalities for differences of means of Hilbert space operators

Linear Algebra and its Applications, 2012

We prove several eigenvalue inequalities for the differences of various means of two positive inv... more We prove several eigenvalue inequalities for the differences of various means of two positive invertible operators A and B on a separable Hilbert space, under the assumption that A − B is compact. Equality conditions of these inequalities are also obtained.

Research paper thumbnail of Multiple Hilbert and Hardy-Hilbert inequalities with non-conjugate parameters

Bulletin of the Australian Mathematical Society, 2005

The main objective of this paper is a study of some new generalisations of Hilbert and Hardy-Hilb... more The main objective of this paper is a study of some new generalisations of Hilbert and Hardy-Hilbert type inequalities involving non-conjugate parameters. We prove general forms of multiple Hilbert-type inequalities, and we also introduce multiple inequalities of Hardy-Hilbert type with non-conjugate parameters.

Research paper thumbnail of A Hilbert inequality and an Euler-Maclaurin summation formula

The ANZIAM Journal, 2007

ABSTRACT

Research paper thumbnail of On a more accurate class of discrete Hilbert-type inequalities

Applied Mathematics and Computation, 2014

Motivated by some known results regarding a particular set of non-homogeneous kernels, in this ar... more Motivated by some known results regarding a particular set of non-homogeneous kernels, in this article we study a more general class of discrete Hilbert-type inequalities. We derive a more accurate form for this class of inequalities, based on the application of the Hermite-Hadamard inequality.

Research paper thumbnail of Hardy-Hilbert Type Inequalities with Fractional Kernel in $ R^ n$

emis.ams.org

Peer reviewed international journal in mathematical inequalities and their applications. Papers a... more Peer reviewed international journal in mathematical inequalities and their applications. Papers are available online in PDF format.

Research paper thumbnail of On a multidimensional version of the Hilbert type inequality

Analysis Mathematica, 2012

ABSTRACT The main objective of this paper is a study of some new multidimensional Hilbert type in... more ABSTRACT The main objective of this paper is a study of some new multidimensional Hilbert type inequalities with a general homogeneous kernel. We derive a pair of equivalent inequalities, and also establish the conditions under which the constant factors included in the obtained inequalities are the best possible. Some applications in particular settings are also considered.

Research paper thumbnail of Jessen's functional, its properties and applications

Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2012

In this paper we consider Jessen's functional, defined by means of a positive isotonic linear fun... more In this paper we consider Jessen's functional, defined by means of a positive isotonic linear functional, and investigate its properties. Derived results are then applied to weighted generalized power means, which yields extensions of some recent results, known from the literature. In particular, we obtain the whole series of refinements and converses of numerous classical inequalities such as the arithmetic-geometric mean inequality, Young's inequality and Hölder's inequality.

Research paper thumbnail of Obituary

Research paper thumbnail of Recent advances in Hilbert-type inequalities. A unified treatment of Hilbert-type inequalities

Research paper thumbnail of Some remarks on reverse Hilbert and Hardy-Hilbert type inequalities

Rendiconti del Circolo Matematico di Palermo, 2007

In this paper we obtain an extension of discrete Hilbert's inequality, by using some numerical me... more In this paper we obtain an extension of discrete Hilbert's inequality, by using some numerical methods. We shall obtain, in a similar way as Yang did in , that the parameter from the kernel can be taken from the interval [3/2, 3). We also compare our findings with existing results, known from the literature.

Research paper thumbnail of On some general Hilbert’s inequalities with non-conjugate parameters

Rendiconti del Circolo Matematico di Palermo, 2007

A generalized discrete Hilbert’s and Hardy-Hilbert’s inequality with non-conjugate parameters can... more A generalized discrete Hilbert’s and Hardy-Hilbert’s inequality with non-conjugate parameters can be established by means of Euler-Maclaurin summation formula. We derive some general results for homogeneous functions and compare our results with some previously known from the literature. We also obtain the improvements on some earlier results.

Research paper thumbnail of Discrete Hilbert-type inequalities with general homogeneous kernels

Rendiconti del Circolo Matematico di Palermo, 2011

The main objective of this paper is an unified treatment of discrete Hilbert-type inequalities wi... more The main objective of this paper is an unified treatment of discrete Hilbert-type inequalities with homogeneous kernels. At the beginning, we prove and discuss two equivalent general inequalities of such type. Further, we analyze the conditions which yield the best possible constant factors in obtained inequalities. The obtained results are then applied to various settings considering homogeneous functions of a

Research paper thumbnail of Multidimensional Jensen’s operator on a Hilbert space and applications

Linear Algebra and its Applications, 2012

Motivated by a joint concavity of connections, solidarities and multidimensional weighted geometr... more Motivated by a joint concavity of connections, solidarities and multidimensional weighted geometric mean, in this paper we extend an idea of convexity (concavity) to operator functions of several variables. With the help of established definitions, we introduce the so called multidimensional Jensen's operator and study its properties. In such a way we get the lower and upper bounds for the above mentioned operator, expressed in terms of non-weighted operator of the same type. As an application, we obtain both refinements and converses for operator variants of some well-known classical inequalities. In order to obtain the refinement of Jensen's integral inequality, we also consider an integral analogue of Jensen's operator for functions of one variable.

Research paper thumbnail of Extension of Hilbert's inequality

Journal of Mathematical Analysis and Applications, 2006

In this paper we make some further extensions of discrete Hilbert's inequality by using Euler-Mac... more In this paper we make some further extensions of discrete Hilbert's inequality by using Euler-Maclaurin summation formula. We give the improvements of some previously obtained results and also compare our results with some previously known from the literature.

Research paper thumbnail of Refinements and reverses of means inequalities for Hilbert space operators

Banach Journal of Mathematical Analysis, 2013

In this paper we derive some improvements of means inequalities for Hilbert space operators. More... more In this paper we derive some improvements of means inequalities for Hilbert space operators. More precisely, we obtain refinements and reverses of the arithmetic-geometric operator mean inequality. As an application, we also deduce an improved variant for the refined arithmetic-Heinz mean inequality. We also present some eigenvalue inequalities for differences of certain operator means.

Research paper thumbnail of A Unified Treatment of Half-Discrete Hilbert-Type Inequalities with a Homogeneous Kernel

Mediterranean Journal of Mathematics, 2013

ABSTRACT In this paper we provide a unified treatment of half-discrete Hilbert-type inequalities ... more ABSTRACT In this paper we provide a unified treatment of half-discrete Hilbert-type inequalities with a general homogeneous kernel. The main results are proved for the case of non-conjugate exponents. A special emphasis is given to determining conditions under which these inequalities include the best possible constants. As an application, we consider some operator expressions closely connected to established inequalities. Finally, we also provide improvements of derived half-discrete inequalities by virtue of the Hermite-Hadamard inequality.

Research paper thumbnail of On some higher-dimensional Hilbert's and Hardy-Hilbert's integral inequalities with parameters

Mathematical Inequalities & Applications, 2008

ABSTRACT A higher dimensional Hilbert’s inequality and a higher dimensional Hardy-Hilbert’s inequ... more ABSTRACT A higher dimensional Hilbert’s inequality and a higher dimensional Hardy-Hilbert’s inequality in non-conjugate case are established. It is also shown that in the conjugate case, the constants in the inequalities are best possible under some appropriate conditions.

Research paper thumbnail of General Hilbert-type inequalities with non-conjugate exponents

Mathematical Inequalities & Applications, 2008

ABSTRACT

Research paper thumbnail of GENERALIZATION OF HILBERT AND HARDY–HILBERT INTEGRAL INEQUALITIES

Abstract. The main objective of this paper is a study of some new generalizations of Hilbert’s an... more Abstract. The main objective of this paper is a study of some new generalizations of Hilbert’s and Hardy-Hilbert’s type inequalities. We establish general form of multiple Hilbert-type inequality and we also introduce multiple inequality of Hardy-Hilbert type. Further, the best possible constants are obtained for some general cases. Mathematics subject classification (2000): 26D15.

Research paper thumbnail of Eigenvalue inequalities for differences of means of Hilbert space operators

Linear Algebra and its Applications, 2012

We prove several eigenvalue inequalities for the differences of various means of two positive inv... more We prove several eigenvalue inequalities for the differences of various means of two positive invertible operators A and B on a separable Hilbert space, under the assumption that A − B is compact. Equality conditions of these inequalities are also obtained.

Research paper thumbnail of Multiple Hilbert and Hardy-Hilbert inequalities with non-conjugate parameters

Bulletin of the Australian Mathematical Society, 2005

The main objective of this paper is a study of some new generalisations of Hilbert and Hardy-Hilb... more The main objective of this paper is a study of some new generalisations of Hilbert and Hardy-Hilbert type inequalities involving non-conjugate parameters. We prove general forms of multiple Hilbert-type inequalities, and we also introduce multiple inequalities of Hardy-Hilbert type with non-conjugate parameters.

Research paper thumbnail of A Hilbert inequality and an Euler-Maclaurin summation formula

The ANZIAM Journal, 2007

ABSTRACT

Research paper thumbnail of On a more accurate class of discrete Hilbert-type inequalities

Applied Mathematics and Computation, 2014

Motivated by some known results regarding a particular set of non-homogeneous kernels, in this ar... more Motivated by some known results regarding a particular set of non-homogeneous kernels, in this article we study a more general class of discrete Hilbert-type inequalities. We derive a more accurate form for this class of inequalities, based on the application of the Hermite-Hadamard inequality.

Research paper thumbnail of Hardy-Hilbert Type Inequalities with Fractional Kernel in $ R^ n$

emis.ams.org

Peer reviewed international journal in mathematical inequalities and their applications. Papers a... more Peer reviewed international journal in mathematical inequalities and their applications. Papers are available online in PDF format.

Research paper thumbnail of On a multidimensional version of the Hilbert type inequality

Analysis Mathematica, 2012

ABSTRACT The main objective of this paper is a study of some new multidimensional Hilbert type in... more ABSTRACT The main objective of this paper is a study of some new multidimensional Hilbert type inequalities with a general homogeneous kernel. We derive a pair of equivalent inequalities, and also establish the conditions under which the constant factors included in the obtained inequalities are the best possible. Some applications in particular settings are also considered.