Download or read book Advances in Inequalities of the Schwarz Gr ss and Bessel Type in Inner Product Spaces written by Sever Silvestru Dragomir and published by Nova Publishers. This book was released on 2005 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Hilbert spaces plays a central role in contemporary mathematics with numerous applications for Linear Operators, Partial Differential Equations, in Nonlinear Analysis, Approximation Theory, Optimisation Theory, Numerical Analysis, Probability Theory, Statistics and other fields. The Schwarz, triangle, Bessel, Gram and most recently, Grüss type inequalities have been frequently used as powerful tools in obtaining bounds or estimating the errors for various approximation formulae occurring in the domains mentioned above. Therefore, any new advancement related to these fundamental facts will have a flow of important consequences in the mathematical fields where these inequalities have been used before.
Download or read book Advances in Inequalities of the Schwarz Triangle and Heisenberg Type in Inner Product Spaces written by Sever Silvestru Dragomir and published by Nova Publishers. This book was released on 2007 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inequalities for hermitian forms -- Schwarz related inequalities -- Reverses for the triangle inequality -- Reverses for the continous triangle inequality -- Reverses of the cbs and heisenberg inequalities -- Other inequalities in inner product spaces
Download or read book New Reverses of Schwarz Triangle and Bessel Inequalities in Inner Product Spaces written by S.S. Dragomir and published by . This book was released on 2018 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: New reverses of the Schwarz, triangle and Bessel inequalities in inner product spaces are pointed out. These results complement the recent ones obtained by the author in the earlier paper [13]. Further, they are emploied to establish new Grüss type inequalities. Finally, some natural integral inequalities are stated as well.
Download or read book Operator Inequalities of the Jensen eby ev and Gr ss Type written by Silvestru Sever Dragomir and published by Springer Science & Business Media. This book was released on 2011-11-12 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. 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 book is 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.
Download or read book Discrete Inequalities of the Cauchy Bunyakovsky Schwarz Type written by Sever Silvestru Dragomir and published by . This book was released on 2004 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Cauchy-Bunyakovsky-Schwarz inequality, or for short, the CBS inequality, plays an important role in different branches of Modern Mathematics including Hilbert Spaces Theory, Probability and Statistics, Classical Real and Complex Analysis, Numerical Analysis, Qualitative Theory of Differential Equations and their applications. The main purpose of this book, that is mainly based on a survey paper written by the author in the Journal of Inequalities in Pure and Applied Mathematics is to identify and highlight the discrete inequalities that are connected with the CBS inequality. Provided are refinements, counterparts and reverse results as well as the study of some functional properties of certain mappings that can be naturally associated with this inequality such as superadditivity, supermultiplicity, the strong versions of these and the corresponding monotonicity properties. Many companions and related results both for real and complex numbers are also presented. It was one of the main aims of the book to provide complete proofs for the results considered.
Download or read book Some Bombieri Type Inequalities in Inner Product Spaces written by S.S. Dragomir and published by . This book was released on 2018 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: Companion results to the Bombieri generalisation of Bessel's inequality in inner product spaces are given.
Download or read book A Reverse of Bessel s Inequality in 2 Inner Product Spaces and Some Gr ss Type Related Results with Applications written by S.S. Dragomir and published by . This book was released on 2018 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: A reverse of Bessel's inequality in 2-inner product spaces and companions of Grüss inequality with applications for determinantal integral inequalities are given.
Download or read book The Cauchy Schwarz Master Class written by J. Michael Steele and published by Cambridge University Press. This book was released on 2004-04-26 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lively, problem-oriented text, first published in 2004, is designed to coach readers toward mastery of the most fundamental mathematical inequalities. With the Cauchy-Schwarz inequality as the initial guide, the reader is led through a sequence of fascinating problems whose solutions are presented as they might have been discovered - either by one of history's famous mathematicians or by the reader. The problems emphasize beauty and surprise, but along the way readers will find systematic coverage of the geometry of squares, convexity, the ladder of power means, majorization, Schur convexity, exponential sums, and the inequalities of Hölder, Hilbert, and Hardy. The text is accessible to anyone who knows calculus and who cares about solving problems. It is well suited to self-study, directed study, or as a supplement to courses in analysis, probability, and combinatorics.
Download or read book Some Boas Bellman Type Inequalities in 2 Inner Product Spaces written by S.S. Dragomir and published by . This book was released on 2018 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some inequalities in 2-inner product spaces generalizing Bessel's result that are similar to the Boas-Bellman inequality from inner product spaces, are given. Applications for determinantal integral inequalities are also provided.
Download or read book Some Pe ari s Type Inequalities in 2 Inner Product Spaces and Applications written by Y.J. Cho and published by . This book was released on 2018 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some results related to the Pečarić's type generalisation of Bessel's inequality in 2-inner product spaces are given. Applications for determinantal integral inequalities are also provided.
Download or read book Some Reverses of the Cauchy Bunyakovsky Schwarz Inequality in 2 Inner Product Spaces written by Sever S. Dragomir and published by . This book was released on 2018 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, some reverses of the Cauchy-Bunyakovsky-Schwarz inequality in 2-inner product spaces are given. Using this framework, some applications for determinantal integral inequalities are also provided.
Download or read book Refinements of Some Reverses of Schwarz s Inequality in 2 Inner Product Spaces and Applications for Integrals written by P. Cerone and published by . This book was released on 2018 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: Refinements of some recent reverse inequalities for the celebrated Cauchy-Bunyakovsky-Schwarz inequality in 2--inner product spaces are given. Using this framework, applications for determinantal integral inequalities are also provided.
Download or read book Some Gr ss Type Inequalities in Inner Product Spaces written by S.S. Dragomir and published by . This book was released on 2018 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some new Grüss type inequalities in inner product spaces and applications for integrals are given.
Download or read book Some Results About Reverses of Cauchy Schwarz Inequality in Inner Product Spaces written by Wang Gong-bao and published by . This book was released on 2018 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some new reverses of the Cauchy-Schwarz inequality in inner product spaces are presented in this paper. As an application of the main result, a formula for error estimate concerning Cauchy-Schwarz's inequality is provided. The results obtained here complement the recent work of the references.
Download or read book Some Bombieri Selberg and Heilbronn Type Inequalities in 2 Inner Product Spaces written by N.S. Barnett and published by . This book was released on 2018 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some results related to the Bombieri type generalisation of Bessel's inequality in 2-inner product spaces are given. The corresponding versions for Selberg and Heilbronn inequalities for 2-inner products and applications for determinantal integral inequalities are also pointed out.
Download or read book Gr ss Type Discrete Inequalities in Inner Product Spaces Revisited written by Sever S. Dragomir and published by . This book was released on 2018 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some sharp inequalities of Grüss type for sequences of vectors in real or complex inner product spaces are obtained. Applications for Jensen's inequality for convex functions defined on such spaces are also provided.
Download or read book On the Bombieri Inequality in Inner Product Spaces written by S.S. Dragomir and published by . This book was released on 2018 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: New results related to the Bombieri generalisation of Bessel's inequality in inner product spaces are given.
