Lacunary ideal summability and its applications to approximation theorem

  • Bipan Hazarika
  • Ayhan EsiEmail author
Original Research Paper


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.


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

Mathematics Subject Classification

40G15 40A99 41A10 41A25 



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Copyright information

© Forum D'Analystes, Chennai 2018

Authors and Affiliations

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

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