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Topological degree theory and fixed point theorems in probabilistic metric spaces

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Abstract

The Leray-Schauder topological degree theory is established in the probabilistic linear normed spaces. Based on this theory, some fixed point theorems for mappings in the probabilistic linear normed spaces are shown.

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References

  1. Schweizer, B. and A. Sklar, Statistical metric spaces,Pacific J. Math.,10 (1960), 313–334.

    Google Scholar 

  2. Schweizer, B. and A. Sklar,Probabilistic Metric Spaces, North-Holland (1983).

  3. Nagumo, M., Degree of mapping in convex linear topological spaces,Amer. J. Math.,73 (1951), 497–511.

    Google Scholar 

  4. Deimling, K.,Nonlinear Functional Analysis, Springer-Verlag (1985).

  5. Sherwood, H., OnE-spaces and their relation to other classes of probabilistic metric spaces,J. London Math. Soc.,44 (1969), 441–448.

    Google Scholar 

  6. Bocsan, G., On some measures of noncompactness in probabilistic metric spaces,Proc. Fifth Conf. Probability Theory, Brasov (1974), 163–168; Bucharest Acad. R.S.R. (1977).

  7. Istratescu, I., A fixed point theorem for mappings with a probabilistic contractive iteration,Rev. Roumaine Math. Pure Appl.,26 (1981), 431–435.

    Google Scholar 

  8. Sehgal, V.M. and A.T. Bharucha-Reid, Fixed point of contraction mapping on probabilistic metric spaces,Math. Systems Theory,6, 2 (1972), 97–102.

    Article  Google Scholar 

  9. Lin Xi, A class of probabilistic linear normed spaces and random operators,Kexae Tongbao,24 (1983), 199–201. (in Chinese)

    Google Scholar 

  10. Zhang Shi-sheng,Fixed Point Theory and Application, Chongqing Press, Chongqing (1984). (in Chinese)

    Google Scholar 

  11. Zhang Shi-sheng, Theory and applications of random operators in probabilistic metric spaces,Acta Math. Appl. Sinica,9, 2 (1986), 129–137. (in Chinese)

    Google Scholar 

  12. Guo Da-jun, A new fixed point theorem,Acta Math. Sinica,24 (1981), 444–450. (in Chinese)

    Google Scholar 

  13. Zhang Shi-sheng, Fixed point theorems of mappings on probabilistic metric spaces with applications,Scientia Sinica (Series A),6 (1983), 495–504. (in Chinese)

    Google Scholar 

  14. Zhang Shi-sheng, On the theory of probabilistic metric spaces with applications,Acta Math. Sinica, New Series,1, 4 (1985), 366–377.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Chengdu

    Zhang Shi-sheng & Chen Yu-qing

Authors
  1. Zhang Shi-sheng
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  2. Chen Yu-qing
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The projects supported by National Natural Science Foundation of China.

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Shi-sheng, Z., Yu-qing, C. Topological degree theory and fixed point theorems in probabilistic metric spaces. Appl Math Mech 10, 495–505 (1989). https://doi.org/10.1007/BF02017893

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  • DOI: https://doi.org/10.1007/BF02017893

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