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

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:

• Korovkin approximation
• approximation of vector-valued functions
• approximation of set-valued functions

AMS Subject Classifications:

• 41A65
• 41A36
• 41A25
• 41A63

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

Work performed under the auspices of GNAMPA (INdAM), Italy.