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Keywords:
generalized metric space; multivalued contraction; fixed points
generalized metric space; multivalued contraction; fixed points
Summary:
The purpose of this paper is to prove an existence result for a multivalued Cauchy problem using a fixed point theorem for a multivalued contraction on a generalized complete metric space.
References:
[1] Aubin J.P., Cellina A.: Differential Inclusions. Springer Verlag, Berlin, 1984. MR 0755330 | Zbl 0538.34007
[2] Aumann R.J.: Integrals of set-valued functions. J. Math. Anal. Appl. 12 (1965), 1-12. MR 0185073 | Zbl 0163.06301
[3] Covitz H., Nadler S.B., Jr.: Multivalued contraction mappings in generalized metric spaces. Israel J. Math. 8 (1970), 5-11. MR 0263062
[4] Hiai F., Umegake H.: Integrals, conditional expectations and martingales of multivalued functions. J. Multivariate Anal. 7 (1977), 149-182. MR 0507504
[5] Himmelberg C.J., Van Vleck F.S.: Lipschitzian generalized differential equations. Rend. Sem. Mat. Univ. Parma 48 (1973), 159-169. MR 0340692 | Zbl 0289.49009
[6] Jung C.K.: On generalized complete metric space. Bull. A.M.S. 75 (1969), 113-116. MR 0234446
[7] Kisielewicz M.: Differential Inclusions and Optimal Control. Kluwer Acad. Publ., Dordrecht, 1991. MR 1135796
[8] Kuratowski K., Ryll-Nardzewski C.: A general theorem on selectors. Bull. Polish Acad. Sci. 13 (1965), 397-403. MR 0188994 | Zbl 0152.21403
[9] Luxemburg W.A.J.: On the convergence of successive approximations in the theory of ordinary differential equations, II. Indag. Math. 20 (1958), 540-546. MR 0124554
[10] Petruşel A.: On a theorem by Roman Wegrzyk. Demonstratio Math. 29 (1996), 637-641. MR 1415506
[11] Wegrzyk R.: Fixed point theorems for multivalued functions and their applications to functional equations. Diss. Math. 201 (1982), 1-28. MR 0687277
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