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Proceedings of the American Mathematical Society

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Near derivations and information functions


Authors: John Lawrence, Geoff Mess and Frank Zorzitto
Journal: Proc. Amer. Math. Soc. 76 (1979), 117-122
MSC: Primary 39B20; Secondary 94A17
MathSciNet review: 534400
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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 [Enhancements On Off] (What's this?)

  • [1] J. Aczél and Z. Daróczy, On measures of information and their characterizations, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. Mathematics in Science and Engineering, Vol. 115. MR 0689178
  • [2] Gy. Maksa, Bounded symmetric information functions, C. R. Math. Rep. Acad. Sci. Canada 2 (1980), no. 5, 247–252. MR 588669
  • [3] J. Lawrence, The uniqueness of the nonnegative information function on algebraic extensions, (to appear).

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0534400-5
Article copyright: © Copyright 1979 American Mathematical Society