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Ukrainian Mathematical Journal

, Volume 45, Issue 8, pp 1215–1220 | Cite as

Convergence near a point and the Arzela-Ascoli-type theorems

  • V. I. Kuz'mich
Article
  • 31 Downloads

Abstract

Theorems are proved giving necessary and sufficient conditions for the convergence of a sequence of continuous (differentiable) functions to a continuous (differentiable) function. The concepts of convergence near a point and equipotential convergence near a point are introduced. These concepts are introduced locally; on a segment, they are equivalent to the quasiuniform convergence and to the uniform convergence of a sequence of functions, respectively.

Keywords

Uniform Convergence 
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References

  1. 1.
    N. N. Luzin,Theory of Functions of a Real Variable [in Russian], Uchpedgiz, Moscow (1948).Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • V. I. Kuz'mich
    • 1
  1. 1.Kherson Pedagogical InstituteKherson

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