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Complex Korovkin Theory

  • George A. AnastassiouEmail author
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 886)

Abstract

Let K be a compact convex subspace of \(\mathbb {C}\) and \(C\left( K,\mathbb {C}\right) \) the space of continuous functions from K into \(\mathbb {C}\). We consider bounded linear functionals from \(C\left( K,\mathbb {C}\right) \) into \(\mathbb {C}\) and bounded linear operators from \(C\left( K,\mathbb {C}\right) \) into itself. We assume that these are bounded by companion real positive linear entities, respectively. We study quantitatively the rate of convergence of the approximation of these linearities to the corresponding unit elements. Our results are inequalities of Korovkin type involving the complex modulus of continuity and basic test functions. See also [5]

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Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of MemphisMemphisUSA

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