Effective rates of convergence for Lipschitzian pseudocontractive mappings in general Banach spaces

This paper gives an explicit and effective rate of convergence for an asymptotic regularity result ‖Txn−xn‖→0‖Txn−xn‖→0 due to Chidume and Zegeye in 2004 [14] where (xn)(xn) is a certain perturbed Krasnoselski–Mann iteration schema for Lipschitz pseudocontractive self-mappings TT of closed and convex subsets of a real Banach space. We also give a qualitative strengthening of the theorem by Chidume and Zegeye, by weakening the assumption of the existence of a fixed point. For the bounded case, our bound is polynomial in the data involved.