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

Dhage, B. C.

An. Științ. Univ. Al. I. Cuza Iași, Ser. Nouă, Mat. 49, No. 1, 45-60 (2003).

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)

Keywords:

metrically convex metric space; coincidentally commuting maps; common fixed point theorem

Citations:

Zbl 0239.54032; Zbl 0359.54038; Zbl 0849.47032