Approximating Fixed Points of Nonexpansive Nonself Mappings in CAT(0) Spaces
Worawut Laowang, Bancha Panyanak · Fixed Point Theory and Applications · 2009
Abstract Suppose that "Equation missing" is a nonempty closed convex subset of a complete CAT(0) space "Equation missing" with the nearest point projection "Equation missing" from "Equation missing" onto "Equation missing". Let "Equation missing" be a nonexpansive nonself mapping with "Equation missing". Suppose that "Equation missing" is generated iteratively by "Equation missing", "Equation missing", "Equation missing", where "Equation missing" and "Equation missing" are real sequences in "Equation missing" for some "Equation missing". Then "Equation missing""Equation missing"-converges to some point "Equation missing" in "Equation missing". This is an analog of a result in Banach spaces of Shahzad (2005) and extends a result of Dhompongsa and Panyanak (2008) to the case of nonself mappings.