Fixed point theorems for (L)-type mappings in complete CAT(0) spaces. (English) Zbl 1415.54032
Summary: In this paper, fixed point properties for a class of more generalized nonexpansive mappings called (L)-type mappings are studied in geodesic spaces. Existence of fixed points, demiclosedness principle, a common fixed point theorem of single-valued and set-valued mappings are obtained in the third section. Moreover, in the last section, \(\Delta\)-convergence and strong convergence theorems for (L)-type mappings are proved. Our results extend the fixed point results of T. Suzuki’s results in [J. Math. Anal. Appl. 340, No. 2, 1088–1095 (2008; Zbl 1140.47041)] and E. Llorens Fuster and E. Moreno Gálvez’s results in [Abstr. Appl. Anal. 2011, Article ID 435686, 15 p. (2011; Zbl 1215.47042)].
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54E40 | Special maps on metric spaces |
Keywords:
(L)-type mappings; geodesic spaces; fixed point theorems; common fixed point theorems; three-step iteration schemeReferences:
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