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

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, ∆-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.