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On some Bounds for the Parameter λ in Steffensen's Inequality
PECARIC, JOSIP,KALAMIR, KSENIJA SMOLJAK Department of Mathematics 2015 Kyungpook mathematical journal Vol.55 No.4
The object is to obtain weaker conditions for the parameter ${\lambda}$ in Steffensen's inequality and its generalizations and refinements additionally assuming nonnegativity of the function f. Furthermore, we contribute to the investigation of the Bellman-type inequalites establishing better bounds for the parameter ${\lambda}$.
Iqbal, Sajid,Pecaric, Josip,Samraiz, Muhammad,Tehmeena, Hassan,Tomovski, Zivorad Korean Mathematical Society 2020 대한수학회논문집 Vol.35 No.1
In this article, we establish some new weighted Hardy-type inequalities involving some variants of extended Riemann-Liouville fractional derivative operators, using convex and increasing functions. As special cases of the main results, we obtain the results of [18,19]. We also prove the boundedness of the k-fractional integral operator on L<sub>p</sub>[a, b].
SUPERQUADRATIC FUNCTIONS AND REFINEMENTS OF SOME CLASSICAL INEQUALITIES
Banic, Senka,Pecaric, Josip,Varosanec, Sanja Korean Mathematical Society 2008 대한수학회지 Vol.45 No.2
Using known properties of superquadratic functions we obtain a sequence of inequalities for superquadratic functions such as the Converse and the Reverse Jensen type inequalities, the Giaccardi and the Petrovic type inequalities and Hermite-Hadamard's inequalities. Especially, when the superquadratic function is convex at the same time, then we get refinements of classical known results for convex functions. Some other properties of superquadratic functions are also given.
EXTENDED GENERALIZED MITTAG-LEFFLER FUNCTION APPLIED ON FRACTIONAL INTEGRAL INEQUALITIES
Andric, Maja,Farid, Ghulam,Pecaric, Josip,Siddique, Muhammad Usama Korean Mathematical Society 2020 대한수학회논문집 Vol.35 No.4
This paper presents several fractional generalizations and extensions of known integral inequalities. To obtain these, an extended generalized Mittag-Leffler function and its fractional integral operator are used.
Ma, Qing-Hua,Pecaric, Josip Korean Mathematical Society 2008 대한수학회지 Vol.45 No.1
Some new explicit bounds on the solutions to a class of new nonlinear retarded Volterra-Fredholm type integral inequalities in two independent variables are established, which can be used as effective tools in the study of certain integral equations. Some examples of application are also indicated.
On some new nonlinear retarded integral inequalities with iterated integrals and their applications
Qing-Hua Ma,Josip Pecaric 대한수학회 2008 대한수학회지 Vol.45 No.2
Some new nonlinear retarded integral inequalities of Gronwall- like type are established, which mainly generalized some results given by Cho, Dragomir and Kim (J. Korean Math. Soc. 43 (2006), No. 3, pp. 563–578) and can be used in the analysis of various problems in the theory of certain classes of differential equations and integral equations. Applications examples are also indicated. Some new nonlinear retarded integral inequalities of Gronwall- like type are established, which mainly generalized some results given by Cho, Dragomir and Kim (J. Korean Math. Soc. 43 (2006), No. 3, pp. 563–578) and can be used in the analysis of various problems in the theory of certain classes of differential equations and integral equations. Applications examples are also indicated.
Qing-Hua Ma,Josip Pecaric 대한수학회 2008 대한수학회지 Vol.45 No.1
Some new explicit bounds on the solutions to a class of new nonlinear retarded Volterra-Fredholm type integral inequalities in two independent variables are established, which can be used as effective tools in the study of certain integral equations. Some examples of application are also indicated. Some new explicit bounds on the solutions to a class of new nonlinear retarded Volterra-Fredholm type integral inequalities in two independent variables are established, which can be used as effective tools in the study of certain integral equations. Some examples of application are also indicated.
Superquadratic functions and refinements of some classical inequalities
Senka Banic,Josip Pecaric,Sanja Varosanec 대한수학회 2008 대한수학회지 Vol.45 No.2
Using known properties of superquadratic functions we obtain a sequence of inequalities for superquadratic functions such as the Converse and the Reverse Jensen type inequalities, the Giaccardi and the Petrovic type inequalities and Hermite-Hadamard’s inequalities. Especially, when the superquadratic function is convex at the same time, then we get refinements of classical known results for convex functions. Some other properties of superquadratic functions are also given. Using known properties of superquadratic functions we obtain a sequence of inequalities for superquadratic functions such as the Converse and the Reverse Jensen type inequalities, the Giaccardi and the Petrovic type inequalities and Hermite-Hadamard’s inequalities. Especially, when the superquadratic function is convex at the same time, then we get refinements of classical known results for convex functions. Some other properties of superquadratic functions are also given.
DISCRETE MULTIPLE HILBERT TYPE INEQUALITY WITH NON-HOMOGENEOUS KERNEL
Ban, Biserka Drascic,Pecaric, Josip,Peric, Ivan,Pogany, Tibor Korean Mathematical Society 2010 대한수학회지 Vol.47 No.3
Multiple discrete Hilbert type inequalities are established in the case of non-homogeneous kernel function by means of Laplace integral representation of associated Dirichlet series. Using newly derived integral expressions for the Mordell-Tornheim Zeta function a set of subsequent special cases, interesting by themselves, are obtained as corollaries of the main inequality.
ON THE PARALLELOGRAM LAW AND BOHR'S INEQUALITY IN G-INNER PRODUCT SPACES
조열제,Vera Culjak,Josip Pecaric 한국수학교육학회 2009 純粹 및 應用數學 Vol.16 No.1
In this paper, we give some results which are in connection to the parallelogram law in G-inner product spaces and also prove some results related to Bohr's inequality in G-inner product spaces.