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Korovkin-type approximation in spaces of vector-valued and set-valued functions

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Abstract We consider some Korovkin-type approximation results for sequences of linear continuous operators in spaces of vector-valued and set-valued continuous functions without assuming the existence of the limit operator. Even… Click to show full abstract

Abstract We consider some Korovkin-type approximation results for sequences of linear continuous operators in spaces of vector-valued and set-valued continuous functions without assuming the existence of the limit operator. Even in spaces of real continuous functions, where similar results have already been established, we replace the positivity assumption with a weaker condition. We also give some quantitative estimate of the convergence and some applications where previous results cannot be applied.

Keywords: vector valued; set valued; spaces vector; korovkin type; type approximation; valued set

Journal Title: Applicable Analysis
Year Published: 2019

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