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A generalization of Clarke’s fixed point theorem

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Abstract

This paper proposes a formally stronger set-valued Clarke’s fixed point theorem. By this theorem we can improve a fixed point theorem for weakly inward contraction set-valued mapping of D. Dowing and W.A. Kirk.

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References

  1. Assad, N.A. and Kirk, W.A., Fixed point theorems for set-valued mapping of contractive type,Pac. J. Math.,43 (1972), 553–562.

    Google Scholar 

  2. Clarke, F.H., Pointwise contraction criteria for the existence of fixed points,Canad. Math. Bull.,21 (1978), 7–11.

    MATH  Google Scholar 

  3. ___, Optimization and Nonsmooth Analysis, Wiely-Interscience, New York, 1983.

    MATH  Google Scholar 

  4. Caristi, J., Fixed point theorems for mapping satisfying inwardness conditions,Trans. Amer. Math. Soc.,215 (1976), 241–151.

    Article  MATH  Google Scholar 

  5. Dowing, D. and Kirk, W.A., Fixed point theorems for set-valued mapping in metric and Banach spaces,Math. Japon.,22 (1977), 99–112.

    Google Scholar 

  6. Mohan, C.J. and Ramendra, K.B., Some Topic in Nonlinear Functional Analysis, Halsted Press, New York, 1985.

    Google Scholar 

  7. Papageorgiou, N.S., Random differential inclusions in Banach spaces,J. Differential Equations,65 (1986), 287–303.

    Article  MATH  Google Scholar 

  8. Reich, S., Appsoximate selections, best approximations, fixed points and invarant sets,J. Math. Anal. Appl.,62 (1978), 104–113.

    Article  MATH  Google Scholar 

  9. Shi Shuzhong, Equivalence between Ekeland’s variational principle and Caristi fixed point theorem,Adv. in Math.,16 (1987), 203–206. (Chinese)

    MATH  Google Scholar 

  10. Yanez, C.M., A remark on weakly inward contractions,,Nonlinear Anal. Theory, Method, Appl.,16 (1991), 847–848.

    Article  MATH  Google Scholar 

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Song, W. A generalization of Clarke’s fixed point theorem. Appl. Math. 10, 463–466 (1995). https://doi.org/10.1007/BF02662502

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  • DOI: https://doi.org/10.1007/BF02662502

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