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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Assad, N.A. and Kirk, W.A., Fixed point theorems for set-valued mapping of contractive type,Pac. J. Math.,43 (1972), 553–562.
Clarke, F.H., Pointwise contraction criteria for the existence of fixed points,Canad. Math. Bull.,21 (1978), 7–11.
___, Optimization and Nonsmooth Analysis, Wiely-Interscience, New York, 1983.
Caristi, J., Fixed point theorems for mapping satisfying inwardness conditions,Trans. Amer. Math. Soc.,215 (1976), 241–151.
Dowing, D. and Kirk, W.A., Fixed point theorems for set-valued mapping in metric and Banach spaces,Math. Japon.,22 (1977), 99–112.
Mohan, C.J. and Ramendra, K.B., Some Topic in Nonlinear Functional Analysis, Halsted Press, New York, 1985.
Papageorgiou, N.S., Random differential inclusions in Banach spaces,J. Differential Equations,65 (1986), 287–303.
Reich, S., Appsoximate selections, best approximations, fixed points and invarant sets,J. Math. Anal. Appl.,62 (1978), 104–113.
Shi Shuzhong, Equivalence between Ekeland’s variational principle and Caristi fixed point theorem,Adv. in Math.,16 (1987), 203–206. (Chinese)
Yanez, C.M., A remark on weakly inward contractions,,Nonlinear Anal. Theory, Method, Appl.,16 (1991), 847–848.
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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