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  • © 2012

Operator Inequalities of Ostrowski and Trapezoidal Type

  • Presents recent results concerning Ostrowski and Trapezoidal type inequalities for continuous functions of selfadjoint operators on complex Hilbert spaces

  • Explores the fundamental results for polynomials in a linear operator, continuous functions of selfadjoint operators

  • Includes supplementary material: sn.pub/extras

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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  • ISBN: 978-1-4614-1779-8
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Table of contents (3 chapters)

  1. Front Matter

    Pages i-x
  2. Background for Functions of Selfadjoint Operators

    • Slivestru Sever Dragomir
    Pages 1-9
  3. Inequalities of Ostrowski Type

    • Slivestru Sever Dragomir
    Pages 11-75
  4. Inequalities of Trapezoidal Type

    • Slivestru Sever Dragomir
    Pages 77-112

About this book

Inequalities of Ostrowski and Trapezoidal Type for Functions of Selfadjoint Operators on Hilbert Spaces presents recent results concerning Ostrowski and Trapezoidal type inequalities for continuous functions of bounded Selfadjoint operators on complex Hilbert spaces.

The first chapter recalls some 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. The author also introduces and explores the fundamental results for polynomials in a linear operator, continuous functions of selfadjoint operators that will play a central role throughout the book. The following chapter is devoted to the Ostrowski’s type inequalities, which provide sharp error estimates in approximating the value of a function by its integral mean and can be used to obtain a priory error bounds for different quadrature rules in approximating the Riemann integral by different Riemann sums. The author also presents recent results extending Ostrowski inequality in various directions for continuous functions of selfadjoint operators in complex Hilbert spaces. The final chapter illustrates recent results obtained in extending trapezoidal type inequality in various directions for continuous functions of selfadjoint operators in complex Hilbert spaces. Applications for mid-point inequalities and some elementary functions of operators as also provided.

This book is intended for use by researchers in various fields of Linear Operator Theory and Mathematical Inequalities. As well as postgraduate students and scientists applying inequalities in their specific areas.

Keywords

  • Hilbert Spaces
  • Linear Operator Theory
  • Mathematical Inequalities
  • Ostrowski andTrapezoidal Functions
  • Selfadjoint Operators
  • partial differential equations

Authors and Affiliations

  • , School of Engineering & Science, Victoria University, Melbourne, Australia

    Silvestru Sever Dragomir

Bibliographic Information

Buying options

eBook USD 34.99
Price excludes VAT (USA)
  • ISBN: 978-1-4614-1779-8
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 49.95
Price excludes VAT (USA)