Two-Step Viscosity Approximation Scheme for Variational Inequality in Banach Spaces

Viscosity approximation methods for pseudocontractive mappings in Banach spaces

Strong convergence of implicit viscosity approximation methods for pseudocontractive mappings in Banach spaces Lu-Chuan Ceng a b , Adrian Petruşel c , Mu-Ming Wong d & Su-Jane Yu e a Department of Mathematics, Shanghai Normal University, Shanghai 200234, China b Scientific Computing Key Laboratory of Shanghai Universities, Shanghai, China c Department of Applied Mathematics, Babeş-Bolyai Univer...

Korpelevich's method for variational inequality problems in Banach spaces

We propose a variant of Korpelevich’s method for solving variational inequality problems with operators in Banach spaces. A full convergence analysis of the method is presented under reasonable assumptions on the problem data.

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

Viscosity Approximation Method for Nonexpansive Nonself-mapping and Variational Inequality

Let E be a real reflexive Banach space which has uniformly Gâteaux differentiable norm. Let K be aclosed convex subset of E which is also a sunny nonexpansive retract of E, and T : K → E be nonexpansive mapping satisfying the weakly inward condition and F (T ) = {x ∈ K, Tx = x} 6= ∅, and f : K → K be a contractive mapping. Suppose that x0 ∈ K, {xn} is defined by { xn+1 = αnf(xn) + (1− αn)((1− δ...

New three-step iteration process and fixed point approximation in Banach spaces

‎In this paper we propose a new iteration process‎, ‎called the $K^{ast }$ iteration process‎, ‎for approximation of fixed‎ ‎points‎. ‎We show that our iteration process is faster than the existing well-known iteration processes using numerical examples‎. ‎Stability of the $K^{ast‎}‎$ iteration process is also discussed‎. ‎Finally we prove some weak and strong convergence theorems for Suzuki ge...