On a difference equation arising in a learning-theory model |
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Authors: | Bernard Epstein |
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Institution: | (1) University of New Mexico, USA;(2) Office of Naval Research, USA |
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Abstract: | An analysis is presented of the equationf(x+a)−f(x)=e
−x
{f(x)−f(x−b)}. Herea andb denote arbitrary positive constants, and a solution is sought which satisfies the following conditions:f(−∞)=0,f(+∞)=1, 0≦f(x)≦1. Existence and uniqueness of solution are established, and then an analytical form of the solution is obtained by use
of bilateral Laplace transform.
Research supported by the National Science Foundation, Grant GP-2558. |
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Keywords: | |
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