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

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.