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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Near derivations and information functions
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by John Lawrence, Geoff Mess and Frank Zorzitto PDF
Proc. Amer. Math. Soc. 76 (1979), 117-122 Request permission

Abstract:

Near-derivations $\gamma$ satisfy the conditions $\gamma (xy) = x\gamma (y) + y\gamma (x)$ for $x,y \in R,\gamma (x + y) \geqslant \gamma (x) + \gamma (y)$ for $x,y \geqslant 0,\gamma (x) = 0$ for $x \in Q$. Existence of near-derivations other than derivations is tied in with that of nonnegative information functions and an example of Daróczy and Maksa. Conditions for near-derivations to be derivations are discussed.
References
  • J. Aczél and Z. Daróczy, On measures of information and their characterizations, Mathematics in Science and Engineering, Vol. 115, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0689178
  • Gy. Maksa, Bounded symmetric information functions, C. R. Math. Rep. Acad. Sci. Canada 2 (1980), no. 5, 247–252. MR 588669
  • J. Lawrence, The uniqueness of the nonnegative information function on algebraic extensions, (to appear).
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 76 (1979), 117-122
  • MSC: Primary 39B20; Secondary 94A17
  • DOI: https://doi.org/10.1090/S0002-9939-1979-0534400-5
  • MathSciNet review: 534400