Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces

An intermixed algorithm for strict pseudo-contractions in Hilbert spaces

*Correspondence: [email protected] 2Department of Mathematics and the RINS, Gyeongsang National University, Jinju, 660-701, Korea Full list of author information is available at the end of the article Abstract An intermixed algorithm for two strict pseudo-contractions in Hilbert spaces have been presented. It is shown that the suggested algorithms converge strongly to the fixed points of two str...

Weak and Strong Convergence Theorems for Equilibrium Problems and Countable Strict Pseudocontractions Mappings in Hilbert Space

Strong Convergence Theorems for Equilibrium Problems and k-Strict Pseudocontractions in Hilbert Spaces

and Applied Analysis 3

Strong Convergence Theorems of Viscosity Iterative Methods for a Countable Family of Strict Pseudo-contractions in Banach Spaces

For a countable family {Tn}n 1 of strictly pseudo-contractions, a strong convergence of viscosity iteration is shown in order to find a common fixed point of {Tn}n 1 in either a p-uniformly convex Banach space which admits a weakly continuous duality mapping or a p-uniformly convex Banach space with uniformly Gâteaux differentiable norm. As applications, at the end of the paper we apply our res...

Weak and Strong Convergence Theorems for k-Strictly Pseudo-Contractive in Hilbert Space

LetK be a nonempty closed convex subset of a real Hilbert space H , and assume that Ti : K → H, i = 1, 2...N be a finite family of ki-strictly pseudo-contractive mappings for some 0 ≤ ki ≤ 1 such that ⋂N i=1 F (Ti) = {x ∈ K : x = Tix, i = 1, 2...N} = ∅. For the following iterative algorithm in K, for x1, x ′ 1 ∈ K and u ∈ K, { yn = PK [kxn + (1− k)Σi=1λiTixn] xn+1 = βnxn + (1− βn)yn and { y′ n ...