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On quasinearly subharmonic functions

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Abstract

We recall the definition of quasinearly subharmonic functions, point out that this function class includes, among others, subharmonic functions, quasisubharmonic functions, nearly subharmonic functions and essentially almost subharmonic functions. It is shown that the sum of two quasinearly subharmonic functions may not be quasinearly subharmonic. Moreover, we characterize the harmonicity via quasinearly subharmonicity.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics of the NASU, ul. Dobrovol’skogo 1, Sloviansk, 84100, Ukraine

    O. Dovgoshey

  2. Department of Mathematical Sciences, University of Oulu, P. O. Box 3000, FI—90014, Oulun Yliopisto, Finland

    J. Riihentaus

  3. Department of Physics and Mathematics, University of Eastern Finland, P. O. Box 111, FI—80101, Joensuu, Finland

    J. Riihentaus

Authors
  1. O. Dovgoshey
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  2. J. Riihentaus
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Correspondence to O. Dovgoshey.

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This paper is dedicated to Professor Vladimir Gutlyanskii on the occasion of his 75th anniversary

Submitted by A. I. Aptekarev

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Dovgoshey, O., Riihentaus, J. On quasinearly subharmonic functions. Lobachevskii J Math 38, 245–254 (2017). https://doi.org/10.1134/S1995080217020068

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  • DOI: https://doi.org/10.1134/S1995080217020068

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