In this talk, we will present, in the context of a complete metric space (X, d), several results concerning existence, uniqueness, data dependence, stability properties for the fixed point inclusion x ∈ F(x), as well as various qualitative properties for the fixed point set of a multi-valued contraction F : X —ο X in the sense of Nadler, see [2], [1]. Applications and extensions to other problems of the metric fixed point theory are suggested.

References

[1] H. Covitz, S.B. Nadler jr., Multivalued contraction mappings in generalized metric spaces, Israel J. Math., 8(1970) 5-11.

[2] S.B. Nadler Jr., Multivalued contraction mappings, Pacific J. Math., 30(1969) 475-488.

[3] A. Petrusel, I.A. Rus, M.A. Serban, Basic problems of the metric fixed point theory and the relevance of a metric fixed point theorem for multivalued operators, J. Nonlinear Convex Anal., 15(2014), no.3, 493-513.

[4] A. Petrusel, G. Petrusel, J.C. Yao, Multivalued graph contraction principle, Optimization, 69(2020), no. 7-8, 1541-1556.

[5] A. Petrusel, G. Petrusel, Some variants of the contraction principle for multi-valued operators, generalizations and applications, J. Nonlinear Convex Anal. 20 (2019), no.

10, 2187-2203.