Cauchy's functional equation in the mean

DOI10.1016/0001-8708(84)90010-0zbMath0541.39003OpenAlexW2069760940MaRDI QIDQ794217

Peter D. T. A. Elliott

Publication date: 1984

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(84)90010-0

zbMATH Keywords

stabilityHölder inequalitymeasurabilityadditive functionsCauchy's functional equationapproximate integral equationsvalue distributions

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Arithmetic functions; related numbers; inversion formulas (11A25) Theoretical approximation of solutions to integral equations (45L05) Functional equations and inequalities (39B99)

Related Items (4)

Functional analysis and additive arithmetic functions ⋮ On the asymptoticity aspect of Hyers-Ulam stability of mappings ⋮ Remarks on the Cauchy functional equation and variations of it ⋮ Approximately linear functionals on Hilbert spaces

Cites Work

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• On the distribution of the values of quadratic L-series in the half-plane \(\sigma > 1/2\)
• Approximate isometries of the space of continuous functions
• On the distribution function of additive functions
• Approximately Convex Functions
• On the Stability of Differential Expressions
• On approximate isometries
• On the Stability of the Linear Functional Equation

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