2 results
Search Results
Now showing 1 - 2 of 2
Conference Object Non-Asymptotic Norm Estimates for the Q-Bernstein Operators(Springer New York LLC, 2013) Ostrovska,S.; Özban,A.Y.The aim of this paper is to present new non-asymptotic norm estimates in C[0,1] for the q-Bernstein operators Bn,q in the case q > 1. While for 0 < q ≤ 1, {double pipe}Bn,q{double pipe} = 1 for all n ∈ ℕ, in the case q > 1, the norm {double pipe}Bn,q{double pipe} grows rather rapidly as n → + ∞ and q → + ∞. Both theoretical and numerical comparisons of the new estimates with the previously available ones are carried out. The conditions are determined under which the new estimates are better than the known ones. © Springer Science+Business Media New York 2013.Article Citation - Scopus: 1On Lin’s Condition for Products of Random Variables(B. I. Verkin Institute for Low Temperature Physics and Engineering, 2019) Il’inskii,A.; Ostrovska,S.The paper presents an elaboration of some results on Lin’s conditions. A new proof is given to the fact that if densities of independent random variables ξ 1 and ξ 2 satisfy Lin’s condition, then the same is true for their product. Also, it is shown that without the condition of independence, the statement is no longer valid. © Alexander Il’inskii and Sofiya Ostrovska, 2019.
