Coefficient Estimate of A Uniform Lipschitz Mapping Failing Fixed Point Property on A Class in The Ko ̈the-Toeplitz Duals for Generalized Cesa`ro Difference Sequence Spaces
In 1983, Orhan introduced Cesa`ro Difference Sequence Spaces. Later, various authors generalized them. In this study, we take a generalized Cesa`ro difference sequence spaces and especially we consider their Ko ̈the-Toeplitz Duals. In fact, recalling that Dowling et al. proved that Banach spaces containing isomorphic copies of l1 cannot have the fixed point property for uniform Lipschitz mappings, we work on a well-known invariant mapping defined on a certain class in a Ko ̈the-Toeplitz Dual of a generalized Cesa`ro difference sequence space so that the right shift mapping can be a uniform Lipschitz mapping. For this aim, we find an upper bound estimate of the Lipschitz coefficient. Next, we investigate the second power of the mapping we care so that it can be uniformly Lipschitz while it is supposed to fail the fixed point property on the class we study in those spaces.