Hausdorff Approximations [Paperback]

1 Elements of segment analysis.- ? 1.1. Segment arithmetic.- 1.1.1. Partial orderings.- 1.1.2. Lattice operations.- 1.1.3. Arithmetic operations.- 1.1.3.1. Addition and subtraction.- 1.1.3.2. Multiplication and division.- 1.1.4. Distance and norm.- ? 1.2. Segment sequences.- 1.2.1. Segment limits.- 1.2.2. Theorems on segment limits.- ? 1.3. Segment functions.- 1.3.1. The segment limit of a segment function.- 1.3.2. Segment derivatives.- 1.3.3. Segment continuity.- 1.3.4. H-continuity.- 2 Hausdorff distance.- ? 2.1. Hausdorff distance between subsets of a metric space.- ? 2.2. The metric space F?.- ? 2.3. H-distancein A? and its properties.- ? 2.4. Relationships between uniform distance and the Hausdorff distance.- ? 2.5. The modulus of H-continuity.- ? 2.6. The order of the modulus of H-continuity.- ? 2.7. H-continuity on a subset.- ? 2.8. H-distance with weight.- 3 Linear methods of approximation.- ? 3.1. Convergence of sequences of positive operators.- ? 3.2. The order of approximation of functions by positive linear operators.- ? 3.3. Approximation of periodic functions by positive integral operators.- 3.3.1. The Fejer operator.- 3.3.2 The Jackson operator.- 3.3.3. The generalized Jackson operator.- 3.3.4 The Vall?e-Poussin operator.- ? 3.4. Approximation of functions by positive integral operators on a finite closed interval.- 3.4.1. The Landau operator.- 3.4.2. The generalized Landau operator.- ? 3.5. Approximation of functions by summation formulas on a finite closed interval.- 3.5.1. Bernstein polynomials.- 3.5.2. Fejer inteipolational polynomials.- ? 3.6. Approximation of nonperiodic functions by integral operators on the entire real axis.- 3.6.1 The Fejer operator in the nonperiodic case.- 3.6.2. The generalized Jackson operator in the nonperiodic case.- 3.6.3. The Weierstrass operator.- ? 3.7. Convergence of derivatives of linear operators.- ? 3.8. A-distance.- ? 3.9. Approximation by partial sums of Fourier series.- 4 Best Hausdorff approximations.- ? 4.1lÃO