Viscosity approximation methods for hierarchical optimization problems in CAT ( 0 ) spaces

Viscosity approximation methods for nonexpansive mappings in CAT(0) spaces

The purpose of this paper is to study the strong convergence theorems of Moudafi's viscosity approximation methods for a nonexpansive mapping T in CAT(0) spaces without the property P. For a contraction f on C and t ∈ (0, 1), let x t ∈ C be the unique fixed point of the contraction x → tf (x) ⊕ (1 – t)Tx; i.e., x t = tf (x t) ⊕ (1 – t)Tx t and x n+1 = α n f (x n) ⊕ (1 – α n)Tx n , n ≥ 0, where ...

Strong Convergence of Viscosity Approximation Methods for Nonexpansive Mappings in CAT(0) Spaces

Viscosity approximation methods for nonexpansive mappings in CAT 0 spaces are studied. Consider a nonexpansive self-mapping T of a closed convex subsetC of a CAT 0 spaceX. Suppose that the set Fix T of fixed points of T is nonempty. For a contraction f on C and t ∈ 0, 1 , let xt ∈ C be the unique fixed point of the contraction x → tf x ⊕ 1 − t Tx. We will show that if X is a CAT 0 space satisfy...

Convergence Theorems for -Nonexpansive Mappings in CAT(0) Spaces

In this paper we derive convergence theorems for an -nonexpansive mappingof a nonempty closed and convex subset of a complete CAT(0) space for SP-iterative process and Thianwan's iterative process.

Viscosity Approximation Methods for Equilibrium Problems, Variational Inequality Problems of Infinitely Strict Pseudocontractions in Hilbert Spaces

Viscosity approximation methods for W-mappings in Hilbert space

We suggest a explicit viscosity iterative algorithm for nding a common elementof the set of common xed points for W-mappings which solves somevariational inequality. Also, we prove a strong convergence theorem with somecontrol conditions. Finally, we apply our results to solve the equilibrium problems.Finally, examples and numerical results are also given.