On the domain of Cesàro matrix defined by weighted means in ℓ t ( . ) , and its pre-quasi ideal with some applications

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.