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

Abstract

In this article, we have constructed the sequence space (Ξ(p, r, t))υ by the domain of Cesàro matrix defined by weighted ( ∣ ∣)∞∑∣∣∣∣ l∑∣∣∣∣ tl means in Nakano sequence space ℓ(tl), where t =(tl) and r =(rl) are sequences of positive reals, and υ(f) = pl rz fz, l=0 z=0 with f = (fz) ∈ Ξ(p, r, t). Some geometric and topological actions of (Ξ(p, r, t))υ, the multiplication maps stand-in on (Ξ(p, r, t))υ, and the eigenvalues distribution of operator ideal formed by (Ξ(p, r, t))υ 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.