We show that the convergences of Jungck, JungckMann, Jungck-Ishikawa, Jungck-Noor and Jungck-multistep iteration processes are equivalent for a class of generalized contractivelike operators defined on a Banach space. Our results are generalizations and extensions of the work of Soltuz [20, 21], Zhiqun [23] and some other numerous ones in literature.

In a recent paper, Noor [M. Aslam Noor, New classes of iterative methods for nonlinear equations, Appl. Math. Comput., 2007, doi:10.1016/j.amc:2007], suggested and analyzed a generalized one parameter Halley method for solving nonlinear equations using. In this paper, we modified this method which has fourth order convergence. As special cases, we obtain a family of third-order iterative method...

in this paper, we prove the existence of fixed point for j-type multi-valuedmap t in cat(0) spaces and also we prove the strong convergence theoremsfor ishikawa iteration scheme without using the xed point of involving map.

The classical Ka?anov scheme for the solution of nonlinear variational problems can be interpreted as a fixed point iteration method that updates given approximation by solving linear problem in each step. Based on this observation, we introduce modified Ka ? anov , which allows (adaptive) damping, and, thereby, to derive new convergence analysis under more general assumptions and wider range a...

Many authors have proposed fixed-point algorithms for obtaining a fixed point of G-nonexpansive mappings without using inertial techniques. To improve convergence behavior, some accelerated methods been introduced. The main aim this paper is to use coordinate affine structure create an algorithm with technique countable family in Hilbert space symmetric directed graph G and prove the weak theor...