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metrically convex metric space; multi-valued non-self map; fixed point
A fixed point theorem is proved for non-self multi-valued mappings in a metrically convex complete metric space satisfying a slightly stronger contraction condition than in Rhoades [3] and under a weaker boundary condition than in Itoh [2] and Rhoades [3].
[1] Blumenthal L.M.: Theory and Applications of Distance Geometry. Clarendon Press, Oxford, 1943. MR 0054981 | Zbl 0208.24801
[2] Itoh S.: Multi-valued generalized contraction and fixed point theorems. Comment. Math. Univ. Carolinae 18 (1977), 247-248. MR 0451227
[3] Rhoades B.E.: A fixed point theorem for a multi-valued non-self mappings. Comment. Math. Univ. Carolinae 37 (1996), 401-404. MR 1399013
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