Abstract
The theory of absolute monotone functions, ∅(x), x real, encompasses a specialization of total positivity having the kernel ∅(x + y) totally positive of all orders. In this note we show how these properties can be used to characterize all continuously differentiable positive solutions of the functional equation
subject to the initial condition f(0) = 0, f′(0)= λ > 0.
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References
Karlin, S. and S. M. McGregor, Iteration of Analytic Functions of Several Variables, in Problems in Analysis,R. C. Gunning (ed.), Princeton University Press, New Jersey, 1970.
Karlin, S. and H. M. Taylor, A First Course in Stochastic Processes,Academic Press, California, 1975.
Kuczman, M., B. Choczewski, R. Ger, Iterative Functional Equations,Cambridge University Press, New York, 1990.
Seneta, E., Regular Varying Functions. Lecture Notes in Math. 508,Springer Verlag, Heidelberg, Germany, 1976.
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© 1996 Springer Science+Business Media Dordrecht
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Karlin, S. (1996). Solutions of certain functional equations. In: Gasca, M., Micchelli, C.A. (eds) Total Positivity and Its Applications. Mathematics and Its Applications, vol 359. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8674-0_20
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DOI: https://doi.org/10.1007/978-94-015-8674-0_20
Publisher Name: Springer, Dordrecht
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