التفاصيل البيبلوغرافية
| العنوان: |
On new existence of a unique common solution to a pair of non-linear matrix equations |
| المؤلفون: |
Garai, Hiranmoy, Dey, Lakshmi Kanta, Sintunavarat, Wutiphol, Som, Sumit, Raha, Sayandeepa |
| سنة النشر: |
2020 |
| المجموعة: |
Mathematics |
| مصطلحات موضوعية: |
Mathematics - Functional Analysis |
| الوصف: |
The main goal of this article is to study the existence of a unique positive definite common solution to a pair of matrix equations of the form \begin{eqnarray*} X^r=Q_1 + \displaystyle \sum_{i=1}^{m} {A_i}^*F(X)A_i \mbox{ and } X^s=Q_2 + \displaystyle \sum_{i=1}^{m} {A_i}^*G(X)A_i \end{eqnarray*} where $Q_1,Q_2\in P(n)$, $A_i\in M(n)$ and $F,G:P(n)\to P(n)$ are certain functions and $r,s>1$. In order to achieve our target, we take the help of elegant properties of Thompson metric on the set of all $n \times n$ Hermitian positive definite matrices. To proceed this, we first derive a common fixed point result for a pair of mappings utilizing a certain class of control functions in a metric space. Then, we obtain some sufficient conditions to assure a unique positive definite common solution to the said equations. Finally, to validate our results, we provide a couple of numerical examples with diagrammatic representations of the convergence behaviour of iterative sequences. |
| نوع الوثيقة: |
Working Paper |
| URL الوصول: |
http://arxiv.org/abs/2006.10863 |
| رقم الانضمام: |
edsarx.2006.10863 |
| قاعدة البيانات: |
arXiv |