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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Constructive approximation 8 (1992), S. 187-201 
    ISSN: 1432-0940
    Keywords: 41A25 ; 41A20 ; Degree of approximation ; Monotone approximation ; Polynomials
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove that forf∈L p , 0〈p〈1, andk a positive integer, there exists an algebraic polynomialP n of degree ≤n such that $$\left\| {f - P_n } \right\|_p \leqslant C\omega _k^\varphi \left( {f,\frac{1}{n}} \right)_p $$ whereω k ϕ (f,t)p is the Ditzian-Totik modulus of smoothness off inL p , andC is a constant depending only onk andp. Moreover, iff is nondecreasing andk≤2, then the polynomialP n can also be taken to be nondecreasing.
    Type of Medium: Electronic Resource
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