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Let $K$ be a nonempty closed convex subset of a real Hilbert space $H$ such that $K\pm K\subset K$, $TK\to H$ a $k$-strict pseudo-contraction for some $0\le k<1$ such that $F\left(T\right)=\{x\in Kx=Tx\}\ne \varnothing$. Consider the following iterative algorithm given by $$\forall x_1\in K,x_{n+1}={\alpha }_n\gamma f\left(x_n\right)+{\beta }_n{x}_n+((1-{\beta }_n)I-{\alpha }_{n}A)P_{K}S{x}_n,n\ge 1,$$ where $SK\to H$ is defined by $Sx=kx+(1-k)Tx$, $P_K$ is the metric projection of $H$ onto $K$, $A$ is a strongly positive linear bounded self-adjoint operator, $f$ is a contraction. It is proved that the sequence $\left\{x_n\right\}$ generated by the above iterative algorithm converges strongly to a fixed point of $T$, which solves a variational inequality related...

In this paper, we introduce a general iterative scheme to investigate the problem of finding a common element of the fixed point set of a strict pseudocontraction and the solution set of a variational inequality problem for a relaxed cocoercive mapping by viscosity approximate methods. Strong convergence theorems are established in a real Hilbert space.