Finding Minimum Norm Fixed Point of Nonexpansive Mappings and Applications

Abstract

We construct two new methods for finding the minimum norm fixed point of nonexpansive mappings in Hilbert spaces. Some applications are also included.

Approximation of a common minimum-norm fixed point of a finite family of σ -asymptotically quasi-nonexpansive mappings with applications

“…Our main result generalize and improve the recent results of Zegeye and Shahzad [30]. Our result also extend and improve the known results of Yang et al [27] (Theorems 3.1, 3.2), Yao et al [28] (Theorems 3.1, 3.2) and Cai et al [4] (Theorems 3.1, 3.2) by using the above iterative algorithm for finding a minimum-norm fixed point of a nonexpansive mapping in lies of the implicit and explicit methods. Finally, we furnish an application of our main result to find solution of a minimizer of continuously Fréchet-differentiable convex functional which has the minimization problem.…”

“…In connection with the iterative approximation of the minimum-norm fixed point of a nonexpansive self-mapping T, in 2011, Yang et al [27] introduced an explicit scheme given by…”

Iterative algorithms for finding minimum-norm fixed point of a finite family of nonexpansive mappings and applications

“…If the iterative sequence {T x n } involved in [4] is replaced by {T P C x n }, then the self-mapping T defined on nonempty closed convex cone in [4] could be relaxed to nonempty closed convex set. It is different from those iterative algorithms proposed by Yang et al [25], Tang and Liu [21] introduced a new relaxed implicit and explicit iterative scheme to approximate the minimum-norm fixed point of nonexpansive mappings in a real Hilbert spaces. Sunthrayuth et al [16] proved several iteration schemes converges strongly to a fixed point of nonexpansive mappings T , which is a unique solution of some variational inequalities.…”

“…These iterative algorithms (1.1) and (1.2) can be viewed as a modification of the well-known iterative algorithms of Browder [1] and Halpern [9], respectively. Yang et al [25] proposed two relaxed iterative algorithms below,…”

Iterative algorithm for common minimum-norm fixed point of a finite family of asymptotically nonextensive nonself mappings in Banach spaces

“…It is noticed that the methods studied above are used to approximate the minimum-norm fixed point of S if 0 ∈ C. In order to overcome the difficulties caused by possible exclusion of the origin from C. Yang et al [3] introduced an explicit scheme given by…”