On the domain of Cesàro matrix defined by weighted means in \(\ell_{t(.)}\), and its pre-quasi ideal with some applications
Authors
A. A. Bakery
- Department of Mathematics, College of Science and Arts at Khulis, University of Jeddah, Jeddah, Saudi Arabia.
- JeddahDepartment of Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt.
E. A. E. Mohamed
- Department of Mathematics, College of Science and Arts at Khulis, University of Jeddah, , Jeddah, Saudi Arabia .
- Department of Mathematics, Faculty of Education, Alzaeim Alazhari University, Khartoum, Sudan.
O. K. S. K. Mohamed
- Department of Mathematics, College of Science and Arts at Khulis, University of Jeddah, Jeddah, Saudi Arabia.
- Academy of Engineering and Medical Sciences, Department of Mathematics, Khartoum, Sudan.
Abstract
In this article, we have constructed the sequence space \(\left(\Xi(p,r,t)\right)_{\upsilon}\) by the domain of Cesàro matrix defined by weighted means in Nakano sequence space \(\ell_{(t_{l})}\), where \(t\!=\!(t_{l})\) and \(r\!=\!(r_{l})\) are sequences of positive reals, and \(\upsilon(f)\!=\!\displaystyle\sum^{\infty}_{l=0}\left(p_{l}\left|\sum^{l}_{z=0}r_{z}f_{z}\right|\right)^{t_{l}}\),
with \(f=(f_{z})\in \Xi(p,r,t)\). Some geometric and topological actions of \(\left(\Xi(p,r,t)\right)_{\upsilon}\), the multiplication maps stand-in on \(\left(\Xi(p,r,t)\right)_{\upsilon}\), and the eigenvalues distribution of operator ideal formed by \(\left(\Xi(p,r,t)\right)_{\upsilon}\) and \(s\)-numbers are discussed. We offer the existence of a fixed point of Kannan contraction operator improvised on these spaces. It is curious that various numerical experiments are introduced to present our results. Moreover, a few gilded applications to the existence of solutions of non-linear difference equations are examined.
Share and Cite
ISRP Style
A. A. Bakery, E. A. E. Mohamed, O. K. S. K. Mohamed, On the domain of Cesàro matrix defined by weighted means in \(\ell_{t(.)}\), and its pre-quasi ideal with some applications, Journal of Mathematics and Computer Science, 26 (2022), no. 1, 41--66
AMA Style
Bakery A. A., Mohamed E. A. E., Mohamed O. K. S. K., On the domain of Cesàro matrix defined by weighted means in \(\ell_{t(.)}\), and its pre-quasi ideal with some applications. J Math Comput SCI-JM. (2022); 26(1):41--66
Chicago/Turabian Style
Bakery, A. A., Mohamed, E. A. E., Mohamed, O. K. S. K.. "On the domain of Cesàro matrix defined by weighted means in \(\ell_{t(.)}\), and its pre-quasi ideal with some applications." Journal of Mathematics and Computer Science, 26, no. 1 (2022): 41--66
Keywords
- Cesàro matrix
- weighted means
- \(s\)-numbers
- multiplication operator
- minimum space
- Kannan contraction operator
MSC
- 46B10
- 46B15
- 47B10
- 46C05
- 46E05
- 46E15
- 46E30
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