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

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Ukrainian Mathematical Journal Aims and scope

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.

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References

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

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Authors and Affiliations

  1. Kherson Pedagogical Institute, Kherson

    V. I. Kuz'mich

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  1. V. I. Kuz'mich
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Translated from Ukrainskii Matemahcheskii Zhurnal, Vol. 45, No. 8, pp. 1090–1095, August, 1993.

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Kuz'mich, V.I. Convergence near a point and the Arzela-Ascoli-type theorems. Ukr Math J 45, 1215–1220 (1993). https://doi.org/10.1007/BF01070968

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  • DOI: https://doi.org/10.1007/BF01070968

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