Ukrainian Mathematical Journal

, Volume 52, Issue 2, pp 249–259 | Cite as

A generalization of the rogosinski-rogosinski theorem

  • S. Ya. Dekanov
  • H. O. Mykhalin


We establish necessary and sufficient conditions for numerical functions αj(x), jN, xX, under which the conditions K(f j K(f 1) ∀j≥2 and \(\mathop {\lim }\limits_{U_r } \sum\nolimits_{j = 1}^\infty {\alpha _j (x)f_j (x) = a} \) yield \(\mathop {\lim }\limits_{U_r } f_1 (x) = a.\) The functions fj(x) are uniformly bounded on the set X and take values in a boundedly compact space L, and K(fj) is the kernel of the function fj. The well-known Rogosinski-Rogosinski theorem follows from the proved statements in the case where X = N, α j (x) ≡ αj, and the space L is the m-dimensional Euclidean space.


Compact Space Numerical Function Partial Limit Functional Sequence Closed Convex Hull 
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Copyright information

© Kluwer Academic/Plenum Publishers 2000

Authors and Affiliations

  • S. Ya. Dekanov
  • H. O. Mykhalin

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