Abstract
In this article, we have constructed the sequence space (Xi(p, r, t))(upsilon) by the domain of Ces`aro matrix defined by weighted means in Nakano sequence space l((t iota)), where t=(t iota) and r=(r iota) are sequences of positive reals, and upsilon(f)= Sigma(infinity)(l=0) (p iota vertical bar Sigma(iota)(z=0) r(z)f(z)vertical bar)(t iota), with f = (f(z)) is an element of Xi(p, r, t). Some geometric and topological actions of (Xi(p, r, t))(upsilon), the multiplication maps stand-in on Xi(p, r, t))(upsilon), and the eigenvalues distribution of operator ideal formed by (Xi(p, r, t))(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.