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Articles

On conjugacy by regularly varying functions

Pages 1186-1199 | Received 14 Apr 2015, Accepted 14 Jun 2015, Published online: 25 Aug 2015

References

  • N.H. Bingham, C.M. Goldie, and J.L. Teugels, Regular Variation  [Encyclopedia of Mathematics and its Applications] Vol. 27, Cambridge University Press, Cambridge, 1990.
  • G. Blanton, and John A. Baker, Iteration groups generated by Cn functions, Arch. Math. (Brno) 3, Scripta Fac. Sci. Nat. UJEP Brunensis 18 (1982), pp. 121–127.
  • B. Choczewski, and M. Kuczma, On the ‘indeterminate case’ in the theory of a linear functional equation, Fund. Math. 58 (1966), pp. 163–175.
  • R.R. Coifman, and M. Kuczma, On asymptotically regular solutions of a linear functional equation, Aequat. Math. 2(2–3) (1969), pp. 332–336. doi:10.1007/BF01817718.
  • M. Crum, On two functional equations which occur in the theory of clock-graduation, Quart. J. Math. Oxford Ser. 10(1) (1939), pp. 155–160. doi:10.1093/qmath/os-10.1.155.
  • J. Domsta, Regularly Varying Solutions of Functional Equations in a Single Variable Applications to the Regular Iteration, Uniwersytet Gdański, Gdańsk, 2002.
  • H. Farzadfard, and B. Robati, Simultaneous Abel equations, Aequat. Math. 83(3) (2012), pp. 283–294. doi:10.1007/s00010-011-0109-7.
  • H. Hahn, Reelle Funktionen, Akademische Verlagsgesellschaft, Leipzig, 1932.
  • J. Korevaar, T. van Ardenne–Ehrenfest, and N.G. de Bruijn, A note on slowly oscilating functions, Nieuw Arch.Wisk. 23 (1949), pp. 77–86.
  • M. Kuczma, On the Schröder equation, Dissertationes Math. (Rozprawy Mat.), No. 4 PWN-Polish Scientific Publishers, Warszawa, 1963.
  • M. Kuczma, Functional equations in a single variable, Monografie Matematyczne, T. 46 PWN-Polish Scientific Publishers, Warszawa, 1968.
  • M. Kuczma, Regularly varying solutions of a linear functional equation, J. Austral. Math. Soc. Ser A 22(2) (1976), pp. 135–143. doi:10.1017/S144678870001524X.
  • M. Kuczma, B. Choczewski, and R. Ger, Iterative Functional Equations  [Encyclopedia of Mathematics and its Applications] Vol. 32, Cambridge University Press, Cambridge, 1990.
  • M. Kuczma, and A. Smajdor, Fractional iteration in the class of convex functions, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 16(9) (1968), pp. 717–720.
  • A. Lundberg, On iterated functions with asymptotic conditions at a fixpoint, Ark. Mat. 5(3-4) (1964), pp. 193–206. doi:10.1007/BF02591121.
  • S. Sternberg, Local Cn transformations of the real line, Duke Math. J. 1 (1955), pp. 276–284.
  • E. Seneta, On Koenigs' ratios for iterates of real functions, J. Australian Math. Soc. 10(1-2) (1969), pp. 207–213. doi:10.1017/S1446788700007084.
  • E. Seneta, Regularly Varying Functions  [Lecture Notes in Math. 508] Springer, Berlin, 1976.
  • G. Szekeres, Regular iteration of real and complex functions, Acta Math. 100(3-4) (1958), pp. 203–258. doi:10.1007/BF02559539.
  • J. Tabor, Rational iteration groups, Wyż. Szkoła Ped. Kraków, Rocznik Nauk.-Dydakt., Prace Matematyczne 11 (1985), pp. 153–176.
  • M.C. Zdun, Regular fractional iterations, Aequationes Math. 28(1) (1985), pp. 73–79. doi:10.1007/BF02189394.
  • M.C. Zdun, The structure of iteration groups of continuous functions, Aequat. Math. 46(1-2) (1993), pp. 19–37. doi:10.1007/BF01833995.
  • M.C. Zdun, and P. Solarz, Recent results on iteration theory: iteration groups and semigroups in the real case, Aequat. Math. 87(3) (2014), pp. 201–245. doi:10.1007/s00010-013-0186-x.

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