Gunduz, Birol

Suffcient conditions for the convergence of a new multistep iteration to a common fixed point of a finite family of asymptotically quasi-nonexpansive mappings in the framework of convex metric spaces are obtained. As an application, related results for a new three step iteration are derived. Our convergence results generalize and refine many known results.

Khan, Safeer Hussain; Gunduz, Birol; Akbulut, Sezgin

A solution of nonlinear ϕ-strongly accretive operator equations is found in this paper by using a one-step- two-mappings iterative scheme in arbitrary real Banach spaces. We give an example to validate our main theorem. Our results are different from those of Khan et. al., [S. H. Khan, A. Rafiq, N. Hussain, Fixed Point Theory Appl., 2012 (2012), 10 pages] in view of different and independent iterative schemes in the sense that none reduces to the other but extend and improve the results of Ding [X. P. Ding, Computers Math. Appl., 33 (1997), 7582] and many others.