Fixed point theorems for (L)-type mappings in complete CAT(0) spaces


Jing Zhou - Department of Mathematics, Harbin Institute of Technology, Harbin 150080, P. R. China. Yunan Cui - Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, P. R. China.


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 point theorem, demiclosed principle, common fixed point theorem of single-valued and set-valued 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 Suzuki’s results in 2008 and Llorens-Fuster’s results in 2011.