Demiclosedness principle for total asymptotically nonexpansive mappings in CAT(0) spaces. (English) Zbl 1406.54027

Karapınar, Erdal; Salahifard, Hero; Vaezpour, S. Mansour

J. Appl. Math. 2014, Article ID 738150, 10 p. (2014).

Summary: We prove the demiclosedness principle for a class of mappings which is a generalization of all the forms of nonexpansive, asymptotically nonexpansive, and nearly asymptotically nonexpansive mappings. Moreover, we establish the existence theorem and convergence theorems for modified Ishikawa iterative process in the framework of CAT(0) spaces. Our results generalize, extend, and unify the corresponding results on the topic in the literature.

MSC:

54H25	Fixed-point and coincidence theorems (topological aspects)
54E40	Special maps on metric spaces
47H09	Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47J25	Iterative procedures involving nonlinear operators