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Proceedings of the American Mathematical Society

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

 

 

Some unbounded functions of regular growth


Authors: H. Arthur DeKleine and Vladimir Drobot
Journal: Proc. Amer. Math. Soc. 35 (1972), 471-476
MSC: Primary 34D05
DOI: https://doi.org/10.1090/S0002-9939-1972-0303025-2
MathSciNet review: 0303025
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Abstract: The concept of regular growth for unbounded nondecreasing functions has its origin in the study of the asymptotic behavior of solutions for the second order equation $ u'' + a(t)u = 0$. In this paper we give sufficient conditions for a continuous, differentiable function $ a(t)$ to possess the property that its logarithm increases regularly. We also show that the logarithm of a continuous unbounded concave or convex function increases regularly.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0303025-2
Keywords: Asymptotic behavior, concave, convex, regular growth
Article copyright: © Copyright 1972 American Mathematical Society