I. The Modulus of Smoothness. - 1. Preliminaries. - 2. The K-Functional and the Modulus of Continuity. - 3. K-Functionals and Moduli of Smoothness Other Forms. - 4. Properties of ??r(ft)p. - 5. More General Step-Weight Functions ?. - 6. Weighted Moduli of Smoothness. - II. Applications. - 7. Algebraic Polynomial Approximation. - 8. Weighted Best Polynomial Approximation. - 9. Exponential-Type or Bernstein-Type Operators. - 10. Weighted Approximations by Exponential-Type Operators. - 11. Weighted Polynomial Approximation in LP(R). - 12. Polynomial Approximation in Several Variables. - 13. Comparisons and Conclusions. - A. The Analogue of Definition 5. 3. 1. - B. The Definition of the Weighted Modulus of Smoothness on (01). - References. - List of Symbols. Language: English