Matucci, Serena; Řehák, Pavel Regularly varying sequences and second order difference equations. (English) Zbl 1147.26002 J. Difference Equ. Appl. 14, No. 1, 17-30 (2008). 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. Reviewer: Janos Galambos (Philadelphia) Cited in 18 Documents 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 Keywords:regularly varying sequence; second order difference equation Citations:Zbl 0247.26002 PDFBibTeX XMLCite \textit{S. Matucci} and \textit{P. Řehák}, J. Difference Equ. Appl. 14, No. 1, 17--30 (2008; Zbl 1147.26002) Full Text: DOI References: [1] DOI: 10.1155/9789775945198 · doi:10.1155/9789775945198 [2] Bingham N.H., Encyclopedia of Mathematics and its Applications 27 (1987) [3] DOI: 10.1007/BF01214468 · Zbl 0256.40002 · doi:10.1007/BF01214468 [4] DOI: 10.1016/S0898-1221(01)00249-8 · Zbl 1007.39006 · doi:10.1016/S0898-1221(01)00249-8 [5] DOI: 10.1080/10236190310001634785 · Zbl 1066.39002 · doi:10.1080/10236190310001634785 [6] DOI: 10.1016/j.jmaa.2004.08.005 · Zbl 1069.39001 · doi:10.1016/j.jmaa.2004.08.005 [7] DOI: 10.1016/j.jmaa.2006.05.024 · Zbl 1116.26002 · doi:10.1016/j.jmaa.2006.05.024 [8] DOI: 10.1023/B:SIMJ.0000042475.70494.fd · doi:10.1023/B:SIMJ.0000042475.70494.fd [9] DOI: 10.1007/s10114-005-0684-4 · Zbl 1170.26300 · doi:10.1007/s10114-005-0684-4 [10] Došlý O., Journal of Difference Equations and Applications 9 pp 49– (2003) · doi:10.1080/10236100309487534 [11] Došlý O., Half-Linear Differential Equations (2005) [12] DOI: 10.1090/S0002-9939-1973-0323963-5 · doi:10.1090/S0002-9939-1973-0323963-5 [13] Geluk J.L., Extensions and Tauberian Theorems (1987) [14] Jaroš J., Results in Mathematics 43 pp 129– (2003) · Zbl 1047.34034 · doi:10.1007/BF03322729 [15] DOI: 10.1016/j.na.2005.05.045 · Zbl 1103.34017 · doi:10.1016/j.na.2005.05.045 [16] Karamata J., Mathematica Cluj 3 pp 33– (1930) [17] Marić V., Lecture Notes in Mathematics 1726 (2000) [18] Marić V., Publications of the Mathematical Institute 48 pp 199– (1990) [19] DOI: 10.1023/A:1013790713905 · Zbl 0982.39004 · doi:10.1023/A:1013790713905 [20] DOI: 10.1080/10236190108808284 · Zbl 1009.39012 · doi:10.1080/10236190108808284 [21] Seneta E., Lecture Notes in Mathematics 508 (1976) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.