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Prof. Jadranka Mićić Hot
University of Zagreb, Croatia
Some recent results about Levinson's operator inequality and its converses
The goal of my talk is to present Levinson's inequality and its converses for Hilbert space operators. At fi rst we give general formulations of Levison's operator inequality and its converses for some large class of "3􀀀convex functions at a point c" and normalized positive linear mappings. Consequently, order among quasi- arithmetic operator means is obtained. In addition, we consider the construction of mappings related to Levinson's inequality. Some properties of these mappings are observed: operator convexity, monotonicity and quasi linearity. To obtain these results, we give appropriate mappings related to the Davis-Choi-Jensen operator inequality. Moreover, we consider mappings related to converses of Levinson's operator inequality. As applications, refi nements and extensions of some know inequalities are obtained.
Jadranka Mićić Hot is a Professor of Mathematics at the Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb. She holds a Masters degree in Numerical Mathematics at Faculty of Sciences, University of Belgrade, Serbia and a PhD degree in Functional Analysis at Faculty of Sciences, University of Zagreb, Croatia. She has published more than 60 papers in journals, books and conference proceedings. She has also published 2 books. She is on the editorial board of several journals including Journal of Mathematical Inequalities and International Journal of Universal Mathematics & Mathematical Sciences. She has participated in 35 conferences with several invited talks. Currently, she is interested in theory and problems of Hilbert space operators, operator inequality, diff erential-geometrical structure of operators and operator means. In addtion, she works on numerical solutions to partial diff erential equations, on super-convergence in finite element methods and numerical-analytical fi eld calculation in electrical engineering.
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