About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 639030, 4 pages
http://dx.doi.org/10.1155/2013/639030
Research Article

Generalizations of Fixed-Point Theorems of Altman and Rothe Types

1School of Mechanics and Civil Engineering, China University of Mining & Technology, Xuzhou, Jiangsu 221008, China
2School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, China

Received 19 June 2013; Revised 9 September 2013; Accepted 27 September 2013

Academic Editor: Lishan Liu

Copyright © 2013 Li Sun et al. 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. M. Altman, “A fixed point theorem in Banach space,” Polish Academy of Sciences, vol. 5, pp. 89–92, 1957. View at Zentralblatt MATH · View at MathSciNet
  2. G. Zhang, T. Zhang, and T. Zhang, “Fixed point theorems of Rothe and Altman types about convex-power condensing operator and application,” Applied Mathematics and Computation, vol. 214, no. 2, pp. 618–623, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. G. Li, “The fixed-point index and the fixed-point theorems of k-set-contraction mappings,” Proceedings of the American Mathematical Society, vol. 104, no. 4, pp. 1163–1170, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  4. G.-Z. Li, S.-Y. Xu, and H.-G. Duan, “Fixed point theorems of 1-set-contractive operators in Banach spaces,” Applied Mathematics Letters, vol. 19, no. 5, pp. 403–412, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. S. Xu, “New fixed point theorems for 1-set-contractive operators in Banach spaces,” Nonlinear Analysis. Theory, Methods & Applications, vol. 67, no. 3, pp. 938–944, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. J. X. Sun and X. Y. Zhang, “A fixed point theorem for convex-power condensing operators and its applications to abstract semilinear evolution equations,” Acta Mathematica Sinica. Chinese Series, vol. 48, no. 3, pp. 439–446, 2005. View at MathSciNet
  7. R. D. Nussbaum, “Degree theory for local condensing maps,” Journal of Mathematical Analysis and Applications, vol. 37, pp. 741–766, 1972. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. R. D. Nussbaum, “The fixed point index and asymptotic fixed point theorems for k-set-contractions,” Bulletin of the American Mathematical Society, vol. 75, pp. 490–495, 1969. View at Publisher · View at Google Scholar · View at MathSciNet
  9. J. X. Sun, Nonlinear Functional Analysis and Its Application, Science Press, Beijing, China, 2007, Chinese.
  10. H. Amann, “Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces,” SIAM Review, vol. 18, no. 4, pp. 620–709, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. D. J. Guo and J. X. Sun, “The calculation of topological degree and its applications,” Journal of Mathematical Research and Exposition, vol. 8, no. 3, pp. 469–480, 1988. View at MathSciNet
  12. W. V. Petryshyn, “Remarks on condensing and k-set-contractive mappings,” Journal of Mathematical Analysis and Applications, vol. 39, pp. 717–741, 1972. View at Publisher · View at Google Scholar · View at MathSciNet