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Global attractivity results for a class of matrix difference equations | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 13، Special Issue for selected papers of ICDACT-2021، خرداد 2022، صفحه 1-15 اصل مقاله (522.37 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.6326 | ||
| نویسندگان | ||
| Sourav Shil؛ Hemant Kumar Nashine* | ||
| Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore-632014, TN, India | ||
| تاریخ دریافت: 24 مرداد 1400، تاریخ بازنگری: 10 دی 1401، تاریخ پذیرش: 11 دی 1400 | ||
| چکیده | ||
| In this chapter, we investigate the global attractivity of the recursive sequence $\{\mathcal{U}_n\} \subset \mathcal{P}(N)$ defined by \[ \mathcal{U}_{n+k} = \mathcal{Q} + \frac{1}{k} \sum_{j=0}^{k-1} \mathcal{A}^* \psi(\mathcal{U}_{n+j}) \mathcal{A}, n=1,2,3\ldots, \] where $\mathcal{P}(N)$ is the set of $N \times N$ Hermitian positive definite matrices, $k$ is a positive integer, $\mathcal{Q}$ is an $N \times N$ Hermitian positive semidefinite matrix, $\mathcal{A}$ is an $N \times N$ nonsingular matrix, $\mathcal{A}^*$ is the conjugate transpose of $\mathcal{A}$ and $\psi : \mathcal{P}(N) \to \mathcal{P}(N)$ is a continuous. For this, we first introduce $\mathcal{FG}$-Pre\v{s}i'c contraction condition for $f: \mathcal{X}^k \to \mathcal{X}$ in metric spaces and study the convergence of the sequence $\{x_n\}$ defined by \[ x_{n+k} = f(x_n, x_{n+1}, \ldots, x_{n+k-1}), n = 1, 2, \ldots \] with the initial values $x_1,\ldots, x_k \in \mathcal{X}$. We furnish our results with some examples throughout the chapter. Finally, we apply these results to obtain matrix difference equations followed by numerical experiments. | ||
| کلیدواژه‌ها | ||
| fixed point approximation؛ iterative method؛ matrix difference equation؛ equilibrium point؛ global attractivity | ||
| مراجع | ||
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