## About The Book

The development of the approximation theory has assisted development in other domains and set the course of completely new directions in mathematics. The approximation theory has a close relationship with functional analysis. In fact, all well-known methods of approximation of functions by means of algebraic or trigonometric polynomials (which are partial sum of Taylor series, interpolating polynomials, Bernstein and Landau polynomials, partial sums of Fourier series, etc.) are linear operators. A successive construction of such a point of view distinguishes the present book from other well-known monographs on approximation theory. This edition has been edited and updated in LaTeX by Dr. Asha Ram Gairola of Doon University to amend some corrections in the original Russian translation as well as introduce minor improvements in the contents

## About The Author

Pavel Petrovich Korovkin was a Russian mathematician whose main fields of research were orthogonal polynomials, approximation theory, and potential theory. In 1947 he proved a generalization of Egorov’s theorem. From the early 1950s, his research interests turned to functional analysis and he examined the convergence and approximation properties of linear positive operators on spaces of continuous functions. The Korovkin approximation is named after him. At Moscow Automobile and Road Institute he headed the department of higher mathematics. He later headed the Department of Mathematical Analysis at Tsiolkovsky State University in Kaluga.

## Table of Contents

**Chapter 1:** Linear Positive Functionals And Operators

**Chapter 2:** Order Of Approximation Of Functions By Means Of Polynomials

**Chapter 3:** Characteristic Of Differential Properties Of A Function With Respect To The Sequence Of Its Best Approximations

**Chapter 4:** Order Of Approximation Of Functions By Means Of Linear Positive Polynomial Operators

**Chapter 5:** Linear Continuous Polynomial Operators

**Chapter 6:** Fourier Series

**Chapter 7:** Interpolating Polynomials

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