# Operator Inequalities of the Jensen, Cebysev and Gruss Type (SpringerBriefs in Mathematics) download epub

#### by **Silvestru Sever Dragomir**

**Epub Book:**1806 kb. |

**Fb2 Book:**1549 kb.

Operator Inequalities of the Jensen, Čebyšev and Grüss Type (SpringerBriefs in Mathematics). Silvestru Sever Dragomir.

Operator Inequalities of the Jensen, Čebyšev and Grüss Type (SpringerBriefs in Mathematics). Download (pdf, . 5 Mb) Donate Read. Epub FB2 mobi txt RTF. Converted file can differ from the original. If possible, download the file in its original format.

Presents recent results concerning inequalities of Jensen, Cebysev and Gruss type for continuous functions .

Presents recent results concerning inequalities of Jensen, Cebysev and Gruss type for continuous functions of bounded selfadjoint operators on complex Hilbert spaces. Illustrates fundamental facts concerning bounded selfadjoint operators on complex Hilbert spaces. The main aim of this book is to present recent results concerning inequalities of the Jensen, Čebyšev and Grüss type for continuous functions of bounded selfadjoint operators on complex Hilbert spaces. In the introductory chapter, the author portrays fundamental facts concerning bounded selfadjoint operators on complex Hilbert spaces. Category: M Mathematics, MC Calculus, MCf Functional analysis. 5 Mb. Operator Inequalities of Ostrowski and Trapezoidal Type. 596 Kb. Operator Inequalities of the Jensen, Cebysev and Gruss Type. 668 Kb. Advances in inequalities for special functions. Pietro Cerone, Sever Silvestru Dragomir.

by Silvestru Sever Dragomir. SpringerBriefs in Mathematics.

These include but are not limited to the operator version of the Dragomir-Ionescu inequality, the Slater type inequalities for operators and its inverses, Jensen’s inequality for twice differentiable functions whose second derivatives satisfy some upper and lower bound conditions and Jensen’s type inequalities for log-convex functions. Hermite-Hadamard’s type inequalities for convex functions and the corresponding results for operator convex functions are also presented. Books related to Operator Inequalities of the Jensen, Čebyšev and Grüss Type. by Silvestru Sever Dragomir.

SpringerBriefs in Mathematics For further volumes: Silvestru Sever Dragomir Operator Inequalities of. .

SpringerBriefs in Mathematics For further volumes: Silvestru Sever Dragomir Operator Inequalities of the Jensen, LCebyLsev and Grüss Type 123 Silvestru Sever Dragomir. 7 Abstract The main aim of this book is to present recent results concerning inequalities of the Jensen, Čebyšev and Grüss ctionsof on complex Hilbert spaces.

from book Operator inequalities of the Jensen, Čebyšev and Grüss type

from book Operator inequalities of the Jensen, Čebyšev and Grüss type. Inequalities of the Čebyšev and Grüss Type. Chapter · September 2012 with 3 Reads. The Čebyšev, or in a different spelling, Chebyshev inequality which compares the integral/discrete mean of the product with the product of the integral/discrete means is famous in the literature devoted to Mathematical Inequalities. It has been extended, generalized, refined, etc. by many authors during the last century.

1School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi, People’s Republic of China. In this paper, some new integral inequalities related to the bounded functions, involving Saigo’s fractional integral operators, are eshtablished. 2Department of Mathematics, Amity University, Jaipur, India. 3Department of Basic Sciences (Mathematics), College of Technology and Engineering, . University of Agriculture and Technology, Udaipur, India. Special cases of the main results are also pointed out. Keywords. Integral inequalities, Gauss hypergeometric function, Saigo’s fractional integral operators.

Sever Silvestru Dragomir's Documents. Advances in Inequalities of the Schwarz, Triangle and Heisenberg Type in Inner Product Spaces. Operator Inequalities of the Jensen, Čebyšev and Grüss Type (SpringerBriefs in Mathematics). Some Gronwall Type Inequalities and Applications.

The main aim of this bookis to present recent results concerning inequalities of the Jensen, Čebyšev and Grüss type for continuous functions of bounded selfadjoint operators on complex Hilbert spaces.

In the introductory chapter, the author portrays fundamental facts concerning bounded selfadjoint operators on complex Hilbert spaces. The generalized Schwarz’s inequality for positive selfadjoint operators as well as some results for the spectrum of this class of operators are presented. This text introduces the reader to the fundamental results for polynomials in a linear operator, continuous functions of selfadjoint operators as well as the step functions of selfadjoint operators. The spectral decomposition for this class of operators, which play a central role in the rest of the book and its consequences are introduced. At the end of the chapter, some classical operator inequalities are presented as well.

Recent new results that deal with different aspects of the famous Jensen operator inequality are explored through the second chapter. These include but are not limited to the operator version of the Dragomir-Ionescu inequality, the Slater type inequalities for operators and its inverses, Jensen’s inequality for twice differentiable functions whose second derivatives satisfy some upper and lower bound conditions and Jensen’s type inequalities for log-convex functions. Hermite-Hadamard’s type inequalities for convex functions and the corresponding results for operator convex functions are also presented.

The Čebyšev, (Chebyshev) inequality that compares the integral/discrete mean of the product with the product of the integral/discrete means is famous in the literature devoted to Mathematical Inequalities. The sister inequality due to Grüss which provides error bounds for the magnitude of the difference between the integral mean of the product and the product of the integral means has also attracted much interest since it has been discovered in 1935 with more than 200 papers published so far. The last part of the book is devoted to the operator versions of these famous results for continuous functions of selfadjoint operators on complex Hilbert spaces. Various particular cases of interest and related results are presented as well.

This bookis intended for use by both researchers in various fields of Linear Operator Theory and Mathematical Inequalities, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.

**Author:**Silvestru Sever Dragomir

**ISBN:**1461415209

**Category:**Science & Math

**Subcategory:**Mathematics

**Language:**English

**Publisher:**Springer; 1st edition (November 12, 2011)

**Pages:**121 pages