Abstract
We state and prove a theorem showing how iterates of the Volterra
operator can be used to evaluate indeterminate forms of type
Open Access
Iterates of Volterra operators and indeterminate forms
Received10 Feb 2005
Revised06 Jan 2006
Accepted22 Jan 2006
Published27 Apr 2006
References
S. Abe, “A note on the -deformation-theoretic aspect of the generalized entropies in nonextensive physics,” Physics Letters. A, vol. 224, no. 6, pp. 326–330, 1997.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetZ. Daróczy, “Generalized information functions,” Information and Computation, vol. 16, pp. 36–51, 1970.
View at: Google Scholar | Zentralblatt MATH | MathSciNetS. P. Eveson, “Asymptotic behaviour of iterates of Volterra operators on ,” Integral Equations and Operator Theory, vol. 53, no. 3, pp. 331–341, 2005.
View at: Publisher Site | Google Scholar | MathSciNetJ. 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.
View at: Google ScholarD. 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 | Zentralblatt MATH | MathSciNetN. 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 Site | Google Scholar | Zentralblatt MATH | MathSciNetG. Little and J. B. Reade, “Estimates for the norm of the th indefinite integral,” The Bulletin of the London Mathematical Society, vol. 30, no. 5, pp. 539–542, 1998.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetA. 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 Site | Google Scholar | Zentralblatt MATH | MathSciNetB. 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 | MathSciNetB. Thorpe, “The norm of powers of the indefinite integral operator on ,” The Bulletin of the London Mathematical Society, vol. 30, no. 5, pp. 543–548, 1998.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetF. G. Tricomi, Integral Equations, vol. 5 of Pure and Applied Mathematics, Interscience, New York, 1957.
View at: Google Scholar | Zentralblatt MATH | MathSciNetC. Tsallis, “Possible generalization of Boltzmann-Gibbs statistics,” Journal of Statistical Physics, vol. 52, no. 1-2, pp. 479–487, 1988.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetJ. 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 Site | Google Scholar | Zentralblatt MATH | MathSciNetT. 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 | Zentralblatt MATH | MathSciNet
Copyright
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.