Lacunary ideal summability and its applications to approximation theorem

Abstract

An ideal I is a family of subsets of positive integers \(\mathbf {N}\) which is closed under taking finite unions and subsets of its elements. In this paper, we define and study the notion of \(I_{\theta }\)-convergence as a variant of the notion of ideal convergence, where \(\theta = (h_{r})\) is a nondecreasing sequence of positive real numbers. We further apply this notion of summability to prove a Korovkin type approximation theorem.

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Correspondence to Ayhan Esi.

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Hazarika, B., Esi, A. Lacunary ideal summability and its applications to approximation theorem. J Anal 27, 997–1006 (2019). https://doi.org/10.1007/s41478-018-0158-6

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Keywords

  • I-convergence
  • \(\theta\)-convergence
  • Positive linear operator
  • The Korovkin theorem

Mathematics Subject Classification

  • 40G15
  • 40A99
  • 41A10
  • 41A25