Abstract
We introduce an iterative process which converges strongly to a common point of the solution set of a variational inequality problem for a Lipschitzian monotone mapping and the fixed point set of a continuous pseudocontractive mapping in Hilbert spaces. In addition, a numerical example which supports our main result is presented. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.
Highlights
Let C be a subset of a real Hilbert space H
T is called strongly pseudocontractive if there exists k ∈ (, ) such that x – y, Tx – Ty ≤ k x – y, for all x, y ∈ C, and T is said to be a k-strict pseudocontractive if there exists a constant ≤ k < such that x – y, Tx – Ty ≤ x – y – k (I – T)x – (I – T)y, for all x, y ∈ C
Our concern now is the following: can an approximation sequence {xn} be constructed which converges to a common point of the solution set of a variational inequality problem for a monotone mapping and the fixed point set of a continuous pseudocontractive mapping?
Summary
Let C be a subset of a real Hilbert space H. A mapping A is called α-inverse strongly monotone if there exists a positive real number α such that
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