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Regularly varying sequences and second order difference equations. (English) Zbl 1147.26002

J. Galambos and E. Seneta [Proc. Am. Math. Soc. 41, 110–116 (1973; Zbl 0247.26002)] introduced the concept of regularly varying sequences based on the classical concept of regular variation of Karamata. The authors of the present paper develop several properties of regularly vaying sequences, and provide a new characterization and representation of such sequences. This becomes a basic tool for providing regularly varying solutions of difference equations. The last section lists some open problems. The list of references well covers the literature.

MSC:

26A12 Rate of growth of functions, orders of infinity, slowly varying functions
39A11 Stability of difference equations (MSC2000)
39A12 Discrete version of topics in analysis

Citations:

Zbl 0247.26002
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References:

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