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The Journal of Analysis

, Volume 27, Issue 4, pp 1151–1161 | Cite as

On ideal summability and a Korovkin type approximation theorem

  • Bipan Hazarika
  • Ayhan EsiEmail author
Original Research Paper
  • 51 Downloads

Abstract

In this paper, we define and study the notion of \(I_{\lambda }\)-convergence as a variant of the notion of ideal convergence, where \(\lambda =(\lambda _{n})\) is a nondecreasing sequence of positive real numbers such that \(\lambda _{n+1} \le \lambda _{n}+1,\lambda _{1}=1,\lambda _{n}\rightarrow \infty (n\rightarrow \infty ).\) We further apply this notion of summability to prove a Korovkin type approximation theorem.

Keywords

Ideal-convergence de la Vallée–Poussin mean Positive linear operator The Korovkin theorem 

Mathematics Subject Classification

40G15 40A99 41A10 41A25 

Notes

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Copyright information

© Forum D'Analystes, Chennai 2019

Authors and Affiliations

  1. 1.Department of MathematicsRajiv Gandhi UniversityDoimukhIndia
  2. 2.Department of Mathematics, Science and Art FacultyAdıyaman UniversityAdıyamanTurkey

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