Abstract
We have constructed the sequence space (Xi(zeta, t))(upsilon), where zeta = (zeta(l)) is a strictly increasing sequence of positive reals tending to infinity and t = (t(l)) is a sequence of positive reals with 1 <= t(l) < infinity, by the domain of (zeta(l))-Cesaro matrix in the Nakano sequence space l((tl)) equipped with the function upsilon(f) = Sigma(infinity)(l=0)(vertical bar Sigma(l)(z=0)f(z)Delta zeta(z)vertical bar/zeta(l))(tl) for all f = (f(z)) is an element of Xi(zeta, t). Some geometric and topological properties of this sequence space, the multiplication mappings defined on it, and the eigenvalues distribution of operator ideal with s-numbers belonging to this sequence space have been investigated. The existence of a fixed point of a Kannan pre-quasi norm contraction mapping on this sequence space and on its pre- quasi operator ideal formed by (Xi(zeta, t))(upsilon) and s-numbers is presented. Finally, we explain our results by some illustrative examples and applications to the existence of solutions of nonlinear difference equations.