Approximation of common fixed points for a family of finite nonexpansive mappings in Banach space

Strong convergence theorems for strict pseudo-contractions in Hilbert spaces

“…Let the sequence {x n } be generated by the CQ method (3). Assume that the control sequence {α n } is chosen so that α n < 1 for all n. Then {x n } converges strongly to P F (T ) x 0 .…”

An Implicit Viscosity Technique of Nonexpansive Mapping in CAT(0) Spaces

“…For through discussion of CAT(0) spaces and of fundamental role they play in geometry , we refer the reader to Bridson and Haefliger [1]. As we know, iterative methods for finding fixed points of nonexpansive mappings have received vast investigations due to its extensive applications in a variety of applied areas of inverse problem, partial differential equations, image recovery, and signal processing; see [2,3,4,5,6,7,8,9,10] and the references therein. One of the difficulties in carrying out results from Banach space to complete CAT(0) space setting lies in the heavy use of the linear structure of the Banach spaces.…”

Metric projection and convergence theorems for nonexpansive mappings in Hadamard spaces

“…Kirk [9] showed that the fixed point set of a nonexpansive mapping T is nonempty, closed and convex. Iterative methods for finding fixed points of nonexpansive mappings have received vast investigations due to its extensive applications in a variety of applied areas of inverse problem, partial differential equations, image recovery, and signal processing; see [18,17,13,16,15,4,19] and the references therein. One of the difficulties in carrying out results from Banach space to Hadamard space setting lies in the heavy use of the linear structure of the Banach spaces.…”