Convergence and rate of convergence by nonlinear singular integral operators depending on two parameters

Author: Karsli H.  

Publisher: Taylor & Francis Ltd

ISSN: 0003-6811

Source: Applicable Analysis, Vol.85, Iss.6-7, 2006-06, pp. : 781-791

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Abstract

In the present article we investigate both the pointwise convergence and the rate of pointwise convergence of the operators to f ( x 0 ) as ( x , λ )→ ( x 0 , λ 0 ) in L 1 〈 a , b 〉 where 〈 a , b 〉 is an arbitrary interval in R.Here, Λ is a nonempty set of indices with any topology and λ 0 an accumulation point of Λ in this topology.