@article {
author = {Shil, Sourav and Nashine, Hemant},
title = {Global attractivity results for a class of matrix difference equations},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {13},
number = {Special Issue for selected papers of ICDACT-2021},
pages = {1-15},
year = {2022},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2021.6326},
abstract = {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.},
keywords = {fixed point approximation,iterative method,matrix difference equation,equilibrium point,global attractivity},
url = {https://ijnaa.semnan.ac.ir/article_6326.html},
eprint = {https://ijnaa.semnan.ac.ir/article_6326_1b015885785bbe6a2b181e92b6471ed0.pdf}
}