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Common fixed point theorems for coincidentally commuting pairs of nonself mappings in metrically convex metric spaces. (English) Zbl 1073.47522

Summary: In this paper, some common fixed point theorems for coincidentally commuting pairs of nonself single-valued and set-valued maps are proved on closed subsets of a metrically convex metric space under a certain weak commutativity condition and the weaker boundary condition that was used in the papers by N. A. Assad and W. A. Kirk [Pac. J. Math. 43, 553–562 (1972; Zbl 0239.54032)], S. Itoh [Commentat. Math. Univ. Carol. 18, 247–258 (1977; Zbl 0359.54038)], B. E. Rhoades [Commentat. Math. Univ. Carol. 37, No. 2, 401–404 (1996; Zbl 0849.47032)], N. J. Huang and Y. J. Cho [Korean J. Math. Sci. 4, 1–10 (1997; per bibl.)].

MSC:

47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
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