Displaying 1581 – 1600 of 2610

Showing per page

On the rate of approximation in the random sum CLT for dependent variables

Adhir Kumar Basu (1987)

Aplikace matematiky

Capital " O " and lower-case " o " approximations of the expected value of a class of smooth functions ( f C r ( R ) ) of the normalized random partial sums of dependent random variables by the expectation of the corresponding functions of Gaussian random variables are established. The same types of approximation are also obtained for dependent random vectors. This generalizes and improves previous results of the author (1980) and Rychlik and Szynal (1979).

On the size of approximately convex sets in normed spaces

S. Dilworth, Ralph Howard, James Roberts (2000)

Studia Mathematica

Let X be a normed space. A set A ⊆ X is approximately convexif d(ta+(1-t)b,A)≤1 for all a,b ∈ A and t ∈ [0,1]. We prove that every n-dimensional normed space contains approximately convex sets A with ( A , C o ( A ) ) l o g 2 n - 1 and d i a m ( A ) C n ( l n n ) 2 , where ℋ denotes the Hausdorff distance. These estimates are reasonably sharp. For every D>0, we construct worst possible approximately convex sets in C[0,1] such that ℋ(A,Co(A))=(A)=D. Several results pertaining to the Hyers-Ulam stability theorem are also proved.

Currently displaying 1581 – 1600 of 2610