Two step size algorithms for strong convergence for a monotone operator in Banach spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 19، دوره 14، شماره 10، دی 2023، صفحه 217-225 اصل مقاله (384.46 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.27501.3626 | ||
| نویسندگان | ||
| John T. Mendy* ؛ Furmose Mendy | ||
| Mathematics Department, University of The Gambia, Brikama Campus, Gambia | ||
| چکیده | ||
| For $p\geq 2$, let $E$ be a $2$ uniformly smooth and $p$ uniformly convex real Banach spaces and let a mapping $\displaystyle \Phi : E \to E^{*}$ be Lipschitz, and strongly monotone such that $\displaystyle \Phi^{-1}(0)\neq \emptyset$. For an arbitrary $(\{\xi_{1}\}, \{\psi_{1}\})\in E$, we define the sequences $\{\xi_{n}\}$ and $\{\psi_{n}\}$ by \begin{equation*} \left\{ \begin{array}{ll} \psi_{n+1} = J^{-1}(J\xi_{n} - \theta_{n}\Phi\xi_{n}), & \hbox{$n\geq 0$} \\ \xi_{n+1} = J^{-1}(J\psi_{n+1} - \lambda_{n}\Phi\psi_{n+1}), & \hbox{$n\geq 0$} \\ \end{array} \right. \end{equation*} where $\lambda_{n}$ and $\theta_{n}$ are positive real number and $J$ is the duality mapping of $E$. Letting $(\lambda_{n}, \theta_{n})\in (0,\Lambda_{p})$ where $\Lambda_{p} >0$, then $\xi_{n}$ and $\psi_{n}$ converges strongly to $\xi^{*}$, a unique solution of the equation $\Phi \xi = 0$. | ||
| کلیدواژهها | ||
| Lipschitz؛ Equations؛ generalized monotone؛ Bounded | ||
| مراجع | ||
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