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Operator Inequalities of the Jensen, Cebysev and Gruss Type


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-1. Functions of Selfadjoint Operators in Hilbert Spaces (Introduction, Bounded Selfadjoint Operators, Continuous Functions of Selfadjoint Operators, Step Functions of Selfadjoint Operators, The Spectral Decomposition of Selfadjoint Operators, References). -2. Inequalities of the Jensen Type ( Introduction, Reverses of the Jensen Inequality, Some Slater Type Inequalities, Other Inequalities for Convex Functions, Some Jensen Type Inequalities for Twice Differentiable Functions, Some Jensen's Type Inequalities for Log-convex Functions, Hermite-Hadamard's Type Inequalities, Hermite-Hadamard's Type Inequalities for Operator Convex Functions, References). -3. Inequalities of the Cebysev and Gruss Type (Introduction, Cebysev's Inequality, Gruss Inequality, More Inequalities of Gruss Type, More Inequalities for the Cebysev Functional, Bounds for the Cebysev Functional of Lipschitzian Functions, Quasi Gruss Type Inequalities, Two Operator Gruss Type Inequalities, References).


From the reviews:"All the results presented in the book are proved along with the details of the original references where they were first obtained. ... Each Chapter is followed by a list of references used therein, and therefore they are relatively independent and can be read separately. ... I am pleased to recommend the book to readers interested in the latest developments in mathematical and functional analysis, a field of modern mathematics that has grown exponentially in the last few decades." (George A. Anastassiou, SIAM Review, Vol. 55 (1), 2013)"The aim of this monograph is to introduce several extensions of classical inequalities to inequalities of bounded linear operators on a complex Hilbert space. ... This monograph gives a good introduction into basic results in operator theory, and is suitable for undergraduate students. The author presents several operator inequalities, using similar techniques over and again. In this way, the readers may study 'how to develop mathematics' by reading the monograph." (Takeaki Yamazaki, Zentralblatt MATH, Vol. 1242, 2012)

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