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Common fixed point theorems for (sub) compatible and set-valued generalized nonexpansive mappings in complete convex metric spaces

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Abstract

In this paper, using some conditions of (sub) compatibility between a set-valued mapping and a single-valued mapping, we establish a necessary and sufficient condition and a sufficient condition for set-valued generalized nonexpansive mappings to have a unique common fixed point in complete convex metric spaces. The results improve, extend and develop the main results in [2–7].

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References

  1. Sessa, S., On a weak commutativity condition of mappings in fixed point considerations,Publ. Inst. Math.,32, 46 (1982), 149–153.

    MATH  MathSciNet  Google Scholar 

  2. Fisher, B., and S. Sessa On a fixed point theorem of Gregus,Internat. J. Math. & Math. Sci.,9 (1986), 23–28.

    Article  MATH  MathSciNet  Google Scholar 

  3. Gregus, Jr. M., A fixed point theorem in Banach space,Boll. Un. Math. Ital.,17-A, 5 (1980), 193–198.

    MathSciNet  Google Scholar 

  4. Mukherjee, R. N. and V. Verma, A note on a fixed point theorem ofGregus Math. Japon.,33 (1988), 745–749.

    MATH  MathSciNet  Google Scholar 

  5. Jungck, G., ON a fixed point theorem of Fisher and Sessa,Internal. J. Math. & Math. Sci.,13 (1990), 497–500.

    Article  MATH  MathSciNet  Google Scholar 

  6. Li Bing-you, Fixed point theorem of nonexpansive mappings in convex metric spaces,Appl. Math. and Mech. (English Ed.),10, 2 (1989), 183–188.

    MathSciNet  Google Scholar 

  7. Fisher, B., Common fixed points on a Banach space,Chung Juan J. XI (1982), 12–15.

    Google Scholar 

  8. Fisher, B., Common fixed points of mappings and set-valued mappings,Rostock. Math. Kolloq.,18 (1981), 69–77.

    MATH  Google Scholar 

  9. Sessa, S. and B. Fisher, On common fixed points of weakly commuting mappings and set-valued mappings,Internat. J. Math. & Math. Sci.,9 (1986), 323–329.

    Article  MATH  MathSciNet  Google Scholar 

  10. Imdad, M., M. S. Khan, and S. Sessa, On some weak conditions of commutativity in common fixed point theorems,Internat. J. Math. & Math. Sci.,11 (1988), 289–296.

    Article  MATH  MathSciNet  Google Scholar 

  11. Naidu, S. V. R. and J. R. Prasad, Fixed point theorems for a pair of set-valued maps on a metric space,Nonlinear Anal. T.M.A.,10 (1986), 1421–1426.

    Article  MATH  Google Scholar 

  12. Jungck, G., compatibble mappings and common fixed points.Internat. J. Math. & Math. Sci.,9 (1986), 771–779.

    Article  MATH  MathSciNet  Google Scholar 

  13. Liu Li-shan, On common fixed points of single-valued mappings and set-valued mappings,J. Qufu Normal Univ. (N. S.),18, 1 (1992), 6–10. (in Chinese)

    Google Scholar 

  14. Takahashi, W., A convexity in metric space and nonexpansive mappings,Kodai Math. Sem. Kep.,22 (1970), 142–149.

    MATH  Google Scholar 

  15. Guay, M. D., K. L. Singh, and J. H. M. Whitfield, Fixed point theorems for nonexpansive mappings in convex metric spaces,Broceedings Conference on Nonlinear Analysis (Ed. by S.P. Singh and J. H. Burry), Marcel Dekker, Inc., New York,80 (1982), 179–189.

    Google Scholar 

  16. Zhao Han-bin, Existence-theorems of fixed point of average nonexpansive mappings in Banach space,Acta Math. Sinica,22 (1979), 459–469.

    MathSciNet  Google Scholar 

  17. Zhang Shi-sheng,fixed Point Theory with Applications, Chongqing Press, Chongqing (1984). (in Chinese)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Qufu Normal University, Qufu, Shandong

    Liu Li-shan

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  1. Liu Li-shan
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Communicated by Zhang Shi-sheng

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Li-shan, L. Common fixed point theorems for (sub) compatible and set-valued generalized nonexpansive mappings in complete convex metric spaces. Appl Math Mech 14, 685–692 (1993). https://doi.org/10.1007/BF02455390

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  • DOI: https://doi.org/10.1007/BF02455390

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