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convex metric space; nonexpansive type mapping; fixed point
Let $C$ be a closed convex subset of a complete convex metric space $X$. In this paper a class of selfmappings on $C$, which satisfy the nonexpansive type condition $(2)$ below, is introduced and investigated. The main result is that such mappings have a unique fixed point.
[LJC93] LJ. B. Ćirić: On some discontinuous fixed point mappings in convex metric spaces. Czechoslovak Math. J. 43(118) (1993), 319–326. MR 1211753
[LJC74] LJ. B. Ćirić: A generalization of Banach’s contraction principle. Proc. Amer. Math. Soc. 45 (1974), 267–273. DOI 10.2307/2040075
[LJC91] LJ. B. Ćirić: On a common fixed point theorem of a Greguš type. Publ. Inst. Math (Beograd) (49)63 (1991), 174–178. MR 1127395
[MD87] M. L. Diviccaro, B. Fisher, S. Sessa: A common fixed point theorem of Greguš type. Publ. Math. Debrecen 34 (1987), 83–89. MR 0901008
[BF82] B. Fisher: Common fixed points on a Banach space. Chung Yuan J. 11 (1982), 19–26.
[BF86] B. Fisher, S. Sessa: On a fixed point theorem of Greguš. Internat. J. Math. Math. Sci. 9 (1986), no. 1, 23–28. DOI 10.1155/S0161171286000030 | MR 0837098
[MG80] M. Greguš: A fixed point theorem in Banach space. Boll. Un. Mat. Ital. A 5 (1980), 193–198. MR 0562137
[BL89] B. Y. Li: Fixed point theorems of nonexpansive mappings in convex metric spaces. Appl. Math. Mech. (English Ed.) 10 (1989), 183–188. DOI 10.1007/BF02014826
[RM88] R. N. Mukherjea, V. Verma: A note on a fixed point theorem of Greguš. Math. Japon. 33 (1988), 745–749. MR 0972387
[WT70] W. Takahashi: A convexity in metric space and nonexpansive mappings I. Kodai Math. Sem. Rep. 22 (1970), 142–149. DOI 10.2996/kmj/1138846111 | MR 0267565 | Zbl 0268.54048
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