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- W4287329371 abstract "Let $Q$ be a nonempty closed and convex subset of a real Hilbert space $% mathcal{H}$. $T:Qrightarrow Q$ is a nonexpansive mapping which has a least one fixed point. $f:Qrightarrow mathcal{H}$ is a Lipschitzian function, and $% F:Qrightarrow mathcal{H}$ is a Lipschitzian and strongly monotone mapping. We prove, under appropriate conditions on the functions $f$ and $F$, the control real sequences ${alpha _{n}}$ and ${beta _{n}},$ and the error term ${e_{n}},$ that for any starting point $x_{0}$ in $Q,$ the sequence $% {x_{n}}$ generated by the perturbed iterative process [ x_{n+1}=beta _{n}x_{n}+(1-beta _{n})P_{Q}left( alpha _{n}f(x_{n})+(I-alpha _{n}F)Tx_{n}+e_{n}right) ] converges strongly to the unique solution of the variational inequality problem [ text{Find }qin Ctext{ such that }langle F(q)-f(q),x-qrangle geq 0text{ for all }xin C ] where $C=F_{ix}(T)$ is the set of fixed points of $T.$ Our main result unifies and extends many well-known previous results." @default.
- W4287329371 created "2022-07-25" @default.
- W4287329371 creator A5041830478 @default.
- W4287329371 creator A5054435385 @default.
- W4287329371 date "2021-02-11" @default.
- W4287329371 modified "2023-09-26" @default.
- W4287329371 title "On the strong convergence of a perturbed algorithm to the unique solution of a variational inequality problem" @default.
- W4287329371 doi "https://doi.org/10.48550/arxiv.2102.05861" @default.
- W4287329371 hasPublicationYear "2021" @default.
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