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

Karsli H.

Applicable Analysis, vol.85, no.6-7, pp.781-791, 2006 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 85 Issue: 6-7
  • Publication Date: 2006
  • Doi Number: 10.1080/00036810600712665
  • Journal Name: Applicable Analysis
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.781-791
  • Keywords: 2000 Mathematics Subject Classifications: 41A35, 28C10, 41-41, 41A25, 47G10, Haar integral, Locally compact Abelian group, Nonlinear singular integral, Pointwise convergence, Rate of convergence
  • Ankara University Affiliated: Yes

Abstract

In the present article we investigate both the pointwise convergence and the rate of pointwise convergence of the operators (Formula presented.) 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. © 2006, Taylor & Francis Group, LLC.