We use strongly pseudocontraction to regularize the following ill-posed monotone variational inequality: finding a point x∗ with the property x∗ ∈ Fix T such that 〈 I − S x∗, x − x∗〉 ≥ 0, x ∈ Fix T where S, T are two pseudocontractive self-mappings of a closed convex subset C of a Hilbert space with the set of fixed points Fix T / ∅. Assume the solution setΩ of VI is nonempty. In this paper, we...

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...

Assume that F is a nonlinear operator which is Lipschitzian and stronglymonotone on a nonempty closed convex subset C of a real Hilbert space H. Assume also thatΩ is the intersection of the fixed point sets of a finite number of Lipschitzian pseudocontractive self-mappings on C. By combining hybrid steepest-descent method, Mann’s iteration method and projection method, we devise a hybrid iterat...

We propose a hybrid extragradient method for finding a common element of the solution set of a variational inequality problem, the solution set of a general system of variational inequalities, and the fixed-point set of a strictly pseudocontractive mapping in a real Hilbert space. Our hybrid method is based on the well-known extragradient method, viscosity approximation method, and Mann-type it...

We introduce a new three step iterative scheme with errors to approximate the unique common fixed point of a family of three strongly pseudocontractive (accretive) mappings on Banach spaces. Our results are generalizations and improvements of results obtained by several authors in literature. In particular, they generalize and improve the results of Mogbademu and Olaleru [A. A. Mogbademu and J....