Abstract
In this article, the sequence space (Xi(r, t))(nu) has been built by the domain of (r(t))-Cesaro matrix in Nakano sequence space l((tl)), where t = (t(l)) and r = (r(l)) are sequences of positive reals with 1 <= t(l) <infinity, and nu(f) =Sigma(infinity)(l=0)(|Sigma(l)(z=0)r(z)f(z)|/Sigma(l)(z=0)r(z))(tl), with f = (f(z)) epsilon Xi (r, t). Some topological and geometric behavior of (Xi(r, t))(v), the multiplication maps acting on (Xi(r, t))(v), and the eigenvalues distribution of operator ideal constructed by o.or, tTHORNTHORN. and s-numbers have been examined. The existence of a fixed point of Kannan prequasi norm contraction mapping on this sequence space and on its prequasi operator ideal are investigated. Moreover, we indicate our results by some explanative examples and actions to the existence of solutions of nonlinear difference equations.