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International Journal of Mathematics and Mathematical Sciences
Volume 2006, Article ID 29764, 6 pages
http://dx.doi.org/10.1155/IJMMS/2006/29764

Iterates of Volterra operators and indeterminate forms

1Departamento de Matemática, Universidade Federal de Pernambuco, Av. Prof. Luiz Freire, s/n, Cidade Universitária, Recife 50740-540, PE, Brazil
2Observatório Nacional, MCT, Rua General José Cristino 77, São Cristovão, Rio de Janeiro 20921-400, RJ, Brazil
3Instituto de Física, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, Maracanã, Rio de Janeiro 20550-900, RJ, Brazil

Received 10 February 2005; Revised 6 January 2006; Accepted 22 January 2006

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. Abe, “A note on the q-deformation-theoretic aspect of the generalized entropies in nonextensive physics,” Physics Letters. A, vol. 224, no. 6, pp. 326–330, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. Z. Daróczy, “Generalized information functions,” Information and Computation, vol. 16, pp. 36–51, 1970. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. S. P. Eveson, “Asymptotic behaviour of iterates of Volterra operators on Lp(0,1),” Integral Equations and Operator Theory, vol. 53, no. 3, pp. 331–341, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  4. J. Karmeshu, Ed., Entropy Measures, Maximum Entropy Principle and Emerging Applications, J. Karmeshu, Ed., vol. 119 of Studies in Fuzziness and Soft Computing, Springer, Berlin, 2003.
  5. D. Kershaw, “Operator norms of powers of the Volterra operator,” Journal of Integral Equations and Applications, vol. 11, no. 3, pp. 351–362, 1999. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. N. Lao and R. Whitley, “Norms of powers of the Volterra operator,” Integral Equations and Operator Theory, vol. 27, no. 4, pp. 419–425, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. G. Little and J. B. Reade, “Estimates for the norm of the nth indefinite integral,” The Bulletin of the London Mathematical Society, vol. 30, no. 5, pp. 539–542, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. A. R. R. Papa, “On one-parameter-dependent generalizations of Boltzmann-Gibbs statistical mechanics,” Journal of Physics. A. Mathematical and General, vol. 31, no. 23, pp. 5271–5276, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. B. D. Sharma and D. P. Mittal, “New nonadditive measures of entropy for discrete probability distributions,” Journal of Mathematical Sciences, vol. 10, pp. 28–40 (1976), 1975. View at Google Scholar · View at MathSciNet
  10. B. Thorpe, “The norm of powers of the indefinite integral operator on (0,1),” The Bulletin of the London Mathematical Society, vol. 30, no. 5, pp. 543–548, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. F. G. Tricomi, Integral Equations, vol. 5 of Pure and Applied Mathematics, Interscience, New York, 1957. View at Zentralblatt MATH · View at MathSciNet
  12. C. Tsallis, “Possible generalization of Boltzmann-Gibbs statistics,” Journal of Statistical Physics, vol. 52, no. 1-2, pp. 479–487, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. J. C. A. van der Lubbe, Y. Boxma, and D. E. Boekee, “A generalized class of certainty and information measures,” Information Sciences, vol. 32, no. 3, pp. 187–215, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. T. Yamano, “On a simple derivation of a family of nonextensive entropies from information content,” Entropy, vol. 6, no. 4, pp. 364–374, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet