In this paper, we introduce an iteration process for approximating common fixed points of two nonself asymptotically nonexpansive mappings in Banach spaces. Our process contains Mann iteration process and some other processes for nonself mappings but is independent of Ishikawa iteration process. We prove some weak and strong convergence theorems for this iteration process. Our results generaliz...

Let E be a real Banach Space and K a nonempty closed convex (not necessarily bounded) subset of E. Iterative methods for the approximation of fixed points of asymptotically demicontractive mappings T : K → K are constructed using the more general modified Mann and Ishikawa iteration methods with errors. Our results show that a recent result of Osilike [3] (which is itself a generalization of a ...

In this paper, we compute quadratic rates of asymptotic regularity for the Tikhonov–Mann iteration in W-hyperbolic spaces. This is an extension to a nonlinear setting modified Mann defined recently by Boţ, Csetnek and Meier Hilbert Furthermore, show that Douglas–Rachford forward-backward algorithms with Tikhonov regularization terms are special cases, spaces, our iteration.

In this paper, we introduce and study a class of new Picard-Mann iterative methods with mixed errors for common fixed points of two different nonexpansive and contraction operators. We also give convergence and stability analysis of the new Picard-Mann iterative approximation and propose numerical examples to show that the new Picard-Mann iteration converges more effectively than the Picard ite...

Let E be an arbitrary real Banach space andK a nonempty, closed, convex (not necessarily bounded) subset of E. If T is a member of the class of Lipschitz, strongly pseudocontractive maps with Lipschitz constant L ≥ 1, then it is shown that to each Mann iteration there is a Krasnosleskij iteration which converges faster than the Mann iteration. It is also shown that the Mann iteration converges ...