We study convergences of Mann and Ishikawa iteration processes for mappings of asymptotically quasi-nonexpansive type in Banach spaces. 1. Introduction and preliminaries. Let D be a nonempty subset of a real Banach space X and T : D → D a nonlinear mapping. The mapping T is said to be asymptotically quasi-nonexpansive (see [5]) if F(T) = ∅ and there exists a sequence {k n } in [0, ∞) with lim n...

These days Mandelbrot set with transcendental function is an interesting area for mathematicians. New equations have been created for Mandelbrot set using trigonometric, logarithmic and exponential functions. Earlier, Ishikawa iteration has been applied to these equations and generate new fractals named as Relative Superior Mandelbrot Set with transcendental function. In this paper, the Mann it...

In this paper, we study strong convergence as well as stability results for a pair of nonself mappings using Jungck-SP iterative scheme and a certain contractive condition. Moreover, with the help of computer programs in C++, we show that Jungck-SP iterative scheme converges faster than Jungck-Noor, Jungck-Ishikawa and Jungck-Mann iterative schemes through example. General Terms Computational M...

We introduce a new modified Ishikawa iterative process and a new W-mapping for computing fixed points of an infinite family of strict pseudocontractions mapping in the framework of q-uniformly smooth Banach spaces. Then, we establish the strong convergence theorem of the proposed iterative scheme under some mild conditions. The results obtained in this paper extend and improve the recent result...

In this paper, we establish some fixed point theorems in connection with sequences of operators in the Banach space setting for Mann and Ishikawa iterative processes. Our results extend some of the results of Berinde, Bonsall, Nadler and Rus from complete metric space to the Banach space setting.