Applications of the fixed point index in Menger PN-spaces

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• 作者：C. X. Zhu (1) chuanxizhu@126.com
  Q. Y. Li (1) lqywsh@163.com
• 关键词：fixed ; point index – ; probabilistic normed space – ; Menger PN ; space – ; T ; retraction – ; completeness – ; distribution function
• 刊名：Mathematical Notes
• 出版年：2012
• 出版时间：May 2012
• 年：2012
• 卷：91
• 期：5-6
• 页码：725-730
• 全文大小：554.5 KB
• 参考文献：1. Q. Y. Li and C. X. Zhu, “The fixed-point index of nonlinear operators in Menger PN-spaces,” Mat. Zametki 90(1), 104–112 (2011) [Math. Notes 90 (1), 94–101 (2011)].
  2. S. S. Chang, J. C. Yeol, and M. K. Shi, Probabilistic Metric Spaces and Nonlinear Operator Theory (Sichuan Univ. Press, Chengdu, 1994).
  3. S. S. Chang and Y. Q. Chen, “Topological degree theory and fixed point theorems in probabilistic metric spaces,” Appl. Math. Mech. (English Ed.) 10(6), 495–505 (1989).
  4. M. Y. Ye, Research on Some Problems of Nonlinear Operators in the PM-Space, Master’s degree thesis (Nanchang University, 2006).
  5. S. S. Chang, B. S. Lee, Y. J. Cho, Y.Q. Chen, S.M. Kang, and J. S. Jung, “Generalized contraction mapping principle and differential equations in probabilistic metric spaces,” Proc. Amer. Math. Soc. 124(8), 2367–2376 (1996).
  6. Q. Y. Li and C. X. Zhu, “Some new fixed points in a Z-P-S space,” J. Systems Sci. Math. Sci. 28(4), 400–405 (2008).
  7. C. X. Zhu, “Several nonlinear operator problems in the Menger PN-space,” Nonlinear Anal. 65(7), 1281–1284 (2006).
  8. C. X. Zhu, “Generalizations of Krasnoselskii’s theorem and Petryshyn’s theorem,” Appl. Math. Lett. 19(7), 628–632 (2006).
  9. C. X. Zhu and Z. B. Xu, “A class of random operator equations in the Hilbert space,” Acta Math. Sinica (Chin. Ser.) 47(4), 641–646 (2004).
  10. C. X. Zhu, “Some theorems in the X-M-PN Space,” Appl. Math. Mech. (English Ed.) 21(2), 181–184 (2000).
  11. C. X. Zhu and Z. B. Xu, “Inequalities and solution of an operator equation,” Appl. Math. Lett. 21(6), 607–611 (2008).
  12. C. X. Zhu and C. F. Chen, “Calculations of random fixed-point index,” J. Math. Anal. Appl. 339(2), 839–844 (2008).
• 作者单位：1. Nanchang University, Nanchang, Republic of China
• ISSN：1573-8876

文摘

In this paper, applications of the fixed-point index of a nonlinear operator in Menger PN-spaces are given. Theorems on the existence of fixed points of a compact continuous operator are obtained. At the same time, the existence of the solution of a class of differential equations in a complete Menger PN-space is studied, and the theorem on the existence of the solution of a class of differential equations is obtained.