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Asymptotic aspect of Drygas, quadratic and Jensen functional equations in metric abelian groups

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Abstract

The asymptotic stability behavior of Drygas, quadratic and Jensen functional equations is investigated. Indeed, we show that if these equations hold approximately for large arguments with an upper bound \({\varepsilon}\), then they are also valid approximately everywhere with a new upper bound which is a constant multiple of \({\varepsilon}\). These results will be applied to the study of asymptotic properties of Drygas, quadratic and Jensen functional equations. We also obtain some results of hyperstability character for these functional equations.

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  1. Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran

    B. Khosravi, M. B. Moghimi & A. Najati

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  1. B. Khosravi
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  2. M. B. Moghimi
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  3. A. Najati
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Correspondence to M. B. Moghimi.

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Khosravi, B., Moghimi, M.B. & Najati, A. Asymptotic aspect of Drygas, quadratic and Jensen functional equations in metric abelian groups. Acta Math. Hungar. 155, 248–265 (2018). https://doi.org/10.1007/s10474-018-0807-x

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  • DOI: https://doi.org/10.1007/s10474-018-0807-x

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