Approximation of functions

Possibility of Approximation: 1. Basic notions 2. Linear operators 3. Approximation theorems 4. The theorem of Stone 5. Notes Polynomials of Best Approximation: 1. Existence of polynomials of best approximation 2. Characterization of polynomials of best approximation 3. Applications of convexity 4. Chebyshev systems 5. Uniqueness of polynomials of best approximation 6. Chebyshev's theorem 7. Chebyshev polynomials 8. Approximation of some complex functions 9. Notes Properties of Polynomials and Moduli of Continuity: 1. Interpolation 2. Inequalities of Bernstein 3. The inequality of Markov 4. Growth of polynomials in the complex plane 5. Moduli of continuity 6. Moduli of smoothness 7. Classes of functions 8.…