Abstract: | Let {T
n
} be a sequence of linear operators on C0,1], satisfying that {T
n
(e
i
)} converge in C0,1] (not necessarily to e
i
) for i = 0,1,2, where e
i
= t
i
. We prove Korovkin-type theorem and give quantitative results on C
20,1] and C0,1] for such sequences. Furthermore, we define King’s type q-Bernstein operator and give quantitative results for the approximation properties of such operators.
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