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Fixed point theorems of local contraction mappings on menger spaces

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Abstract

In this paper, we introduce the concept of ε-chainable PM-space, and give several fixed point theorems of one-valued and multivalued local contraction mapping on the kind of spaces.

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References

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

    Google Scholar 

  2. Cain, G.L., Jr. and R.H. Kasriel, Fixed and periodic points of local contraction mappings on probabilistic metric spaces, ibid.,9 (1975), 289–297.

    Google Scholar 

  3. Edelstein, M., An extension of Banach's contraction principle,Proc. Amer. Math. Soc.,12 (1961), 7–10.

    Google Scholar 

  4. Kuhfitting, Peter K.F., Fixed points of Locally contractive and nonexpansive set-valued mappings,Pacific J. Math.,65, 2 (1976), 399–403.

    Google Scholar 

  5. Menger, K., Statistical metrics,Proc. Nat. Acad. Sci. USA.,28 (1942), 535–537.

    Google Scholar 

  6. Zhang Shi-sheng, Fixed point theorems of mappings on probabilistic metric spaces with applications,Scientia Sinica (Series A),26, 11 (1983), 1144–1155.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  9. Schweizer, B., A. Sklar and E. Thorp, The metrization of statistical metric spaces,Pacific J. Math.,10 (1960), 673–675.

    Google Scholar 

  10. Fang Jin-xuan, Fixed point theorems for multi-valued mappings on Menger spaces,Journal of Nanjing Normal University (Natural Science Edition),11, 4 (1988), 1–6 (in Chinese)

    Google Scholar 

  11. Fang Jin-xuan, Fixed point theorem of Φ-contraction mapping on probabilistic metric spaces,Journal of Xinjiang University (Natural Science Edition),5, 3 (1988), 21–28. (in Chinese)

    Google Scholar 

  12. Nadler, S. B., Multi-valued contraction mapping,Pacific J. Math.,30 (1969), 475–487.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Nanjing Normal University, Nanjing

    Fang Jin-xuan

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  1. Fang Jin-xuan
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Communicated by Zhang Shi-sheng

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Jin-xuan, F. Fixed point theorems of local contraction mappings on menger spaces. Appl Math Mech 12, 363–372 (1991). https://doi.org/10.1007/BF02020399

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  • DOI: https://doi.org/10.1007/BF02020399

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