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2017 | Book

Self Adjoint Operator Korovkin Type Quantitative Approximation Theory Read chapter Read first chapter

Intelligent Comparisons II: Operator Inequalities and Approximations

Author: George A. Anastassiou

Publisher: Springer International Publishing

Book Series : Studies in Computational Intelligence

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

This compact book focuses on self-adjoint operators’ well-known named inequalities and Korovkin approximation theory, both in a Hilbert space environment. It is the first book to study these aspects, and all chapters are self-contained and can be read independently. Further, each chapter includes an extensive list of references for further reading.
The book’s results are expected to find applications in many areas of pure and applied mathematics. Given its concise format, it is especially suitable for use in related graduate classes and research projects. As such, the book offers a valuable resource for researchers and graduate students alike, as well as a key addition to all science and engineering libraries.

Table of Contents

Frontmatter
Chapter 1. Self Adjoint Operator Korovkin Type Quantitative Approximation Theory
Abstract
Here we present self adjoint operator Korovkin type theorems, via self adjoint operator Shisha-Mond type inequalities. This is a quantitative treatment to determine the degree of self adjoint operator uniform approximation with rates, of sequences of self adjoint operator positive linear operators. We give several applications involving the self adjoint operator Bernstein polynomials. It follows [2].
George A. Anastassiou
Chapter 2. Self Adjoint Operator Korovkin and Polynomial Direct Approximations with Rates
Abstract
Here we present self adjoint operator Korovkin type theorems, via self adjoint operator Shisha-Mond type inequalities, also we give self adjoint operator polynomial approximations. This is a quantitative treatment to determine the degree of self adjoint operator uniform approximation with rates, of sequences of self adjoint operator positive linear operators. The same kind of work is performed over important operator polynomial sequences. Our approach is direct based on Gelfand isometry. It follows [1].
George A. Anastassiou
Chapter 3. Quantitative Self Adjoint Operator Other Direct Approximations
Abstract
Here we give a series of self adjoint operator positive linear operators general results. Then we present specific similar results related to neural networks. This is a quantitative treatment to determine the degree of self adjoint operator uniform approximation with rates, of sequences of self adjoint positive linear operators in general, and in particular of self adjoint specific neural network operators. It follows [4] (Anastassiou, J. Nonlinear Sci. Appl. (2016)).
George A. Anastassiou
Chapter 4. Fractional Self Adjoint Operator Poincaré and Sobolev Inequalities
Abstract
We present here many fractional self adjoint operator Poincaré and Sobolev type inequalities to various directions.
George A. Anastassiou
Chapter 5. Self Adjoint Operator Ostrowski Inequalities
Abstract
We present here several self adjoint operator Ostrowski type inequalities to all directions.
George A. Anastassiou
Chapter 6. Integer and Fractional Self Adjoint Operator Opial Inequalities
Abstract
We present here several integer and fractional self adjoint operator Opial type inequalities to many directions. These are based in the operator order over a Hilbert space. It follows [3].
George A. Anastassiou
Chapter 7. Self Adjoint Operator Chebyshev-Grüss Inequalities
Abstract
We present here very general self adjoint operator Chebyshev-Grüss type inequalities to all cases. We give applications. It follows [2].
George A. Anastassiou
Chapter 8. Ultra General Fractional Self Adjoint Operator Representation Formulae and Operator Poincaré and Sobolev and Other Basic Inequalities
Abstract
We give here many very general fractional self adjoint operator Poincaré and Sobolev type and other basic inner product inequalities to various directions.
George A. Anastassiou
Chapter 9. Harmonic Self Adjoint Operator Chebyshev-Grüss Type Inequalities
Abstract
We present here very general self adjoint operator harmonic Chebyshev-Grüss inequalities with applications.
George A. Anastassiou
Chapter 10. Ultra General Self Adjoint Operator Chebyshev-Grüss Type Inequalities
Abstract
We demonstrate here most general self adjoint operator Chebyshev-Grüss type inequalities to all cases. We finish with applications. It follows [2] (G. Anastassiou, Most General Self Adjoint Operator Chebyshev-Grüss Inequalities (2016).
George A. Anastassiou
Chapter 11. About a Fractional Means Inequality
Abstract
Here we present an interesting fractional means scalar inequality. It follows [2].
George A. Anastassiou
Metadata
Title
Intelligent Comparisons II: Operator Inequalities and Approximations
Author
George A. Anastassiou
Copyright Year
2017
Electronic ISBN
978-3-319-51475-8
Print ISBN
978-3-319-51474-1
DOI
https://doi.org/10.1007/978-3-319-51475-8

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