On the limits of real-valued functions in sets involving $ \psi $-density, and applications

J. Heittokangas; Z. Latreuch; J. Wang; M. A. Zemirni

On the limits of real-valued functions in sets involving $ \psi $-density, and applications

Complex Variables 2020-11-16 v2

Authors: J. Heittokangas , Z. Latreuch , J. Wang , M. A. Zemirni

Abstract

We prove new results on upper and lower limits of real-valued functions by means of $\psi$ -densities introduced by P. D. Barry in 1962. This allows us to improve several existing results on the growth of non-decreasing and unbounded real-valued functions in sets of positive density. The $\psi$ -densities are also used to introduce a new concept of a limit for real-valued functions. The results in this paper are of interest in real analysis as well as in the theory of meromorphic functions.

Keywords

psi-density real-valued functions upper and lower limits positive density meromorphic functions real analysis

Cite

@article{arxiv.2006.02066,
  title  = {On the limits of real-valued functions in sets involving $ \psi $-density, and applications},
  author = {J. Heittokangas and Z. Latreuch and J. Wang and M. A. Zemirni},
  journal= {arXiv preprint arXiv:2006.02066},
  year   = {2020}
}

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15 pages

On the limits of real-valued functions in sets involving $ \psi $-density, and applications

Abstract

Keywords

Cite

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