# Complex Korovkin Theory

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## 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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