In this paper, we obtain a direct result and Voronovskaya type asymptotic formula for the exponential-type operators in simultaneous approximation with polynomial growth. In the end, we obtain the recurrence formulae for the central moments, direct results and Voronovskaya type asymptotic formulae for the various mixed summation-integral type operators. 2000 AMS Subject Classification. 41A28, 4...

Given a family of n convex compact sets in the plane, one can always choose n of them which are either pairwise disjoint or pairwise intersecting. On the other hand, there exists a family of n segments in the plane such that the maximum size of a subfamily with pairwise disjoint or pairwise intersecting elements in n*"* ^ n-.

The little Grothendieck theorem for Banach spaces says that every bounded linear operator between C(K) and l2 is 2-summing. However, it is shown in [7] that the operator space analogue fails. Not every cb-map v : K → OH is completely 2-summing. In this paper, we show an operator space analogue of Maurey’s theorem : Every cb-map v : K → OH is (q, cb)-summing for any q > 2 and hence admits a fact...