Fixed point theorems for Lipschitzian type mappings in CAT(0) spaces

Abstract

The purpose of this paper is to investigate the demiclosedness principle, the existence theorem, and convergence theorems in CAT(0) spaces for a class of mappings which is essentially wider than that of asymptotically nonexpansive mappings. Our results generalize, extend and unify the corresponding results of Dhompongsa and Panyanak [S. Dhompongsa, B. Panyanak, On ▲-convergence theorems in CAT(0) spaces, Comput. Math. Appl., 56 (2008) 2572-2579], Osilike and Aniagbosor [M.O. Osilike, S.C. Aniagbosor, Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings, Math. Computer Model., 32 (2000), 1181-1191], Sahu and Beg [D.R. Sahu, I. Beg, Weak and strong convergence for fixed points of nearly asymptotically non-expansive mappings, Internat. J. Modern Math., 3(2) (2008), 135-151]. © 2011 Elsevier Ltd.