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Quantitative Estimates for Positive Linear Operators in terms of the Usual Second Modulus

2015
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Abstract and Applied Analysis
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We give accurate estimates of the constantsCn(A(I),x)appearing in direct inequalities of the form|Lnf(x)-f(x)|≤Cn(A(I),x)ω2 f;σ(x)/n,f∈A(I),x∈I, and n=1,2,...,whereLnis a positive linear operator reproducing linear functions and acting on real functionsfdefined on the intervalI,A(I)is a certain subset of such functions,ω2(f;·)is the usual second modulus off, andσ(x)is an appropriate weight function. We show that the size of the constantsCn(A(I),x)mainly depends on the degree of smoothness of

doi:10.1155/2015/915358
fatcat:qlfvlw7pqzczda3uuzumbo26pe