Abstract
In this paper, the continuity of the limit q-Bernstein operator with respect to parameter q is investigated. It is proved that the map q↦B q is continuous in the strong operator topology on C[0, 1] for q ∈ [0, 1]. Meanwhile, in the uniform operator topology, this map is discontinuous at every q ∈ [0, 1].
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Almesbahi, M.M., Ostrovska, S., Turan, M. (2019). The Limit q-Bernstein Operators with Varying q . In: Taş, K., Baleanu, D., Machado, J. (eds) Mathematical Methods in Engineering. Nonlinear Systems and Complexity, vol 23. Springer, Cham. https://doi.org/10.1007/978-3-319-91065-9_10
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DOI: https://doi.org/10.1007/978-3-319-91065-9_10
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