In the last three decades many papers have been published on the iterative approximation of fixed points for certain classes of operators, using the Mann and Ishikawa iteration methods, see [4], for a recent survey. These papers were motivated by the fact that, under weaker contractive type conditions, the Picard iteration (or the method of successive approximations), need not converge to the f...

A convergence theorem of Rhoades [18] regarding the approximation of fixed points of some quasi contractive operators in uniformly convex Banach spaces using the Ishikawa iterative procedure, is extended to arbitrary Banach spaces. The conditions on the parameters {αn} that define the Ishikawa iteration are also weakened.

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 ...

In this paper, we establish weak and strong convergence theorems of a two-step modified projection-type Ishikawa iterative scheme to the fixed point α-hemicontractive mappings without any compactness assumption on operator or space. Our results extend, improve generalize several previously known existing literature.

in this paper‎, ‎strong convergence theorems of ishikawa type implicit iteration‎ ‎process with errors for a finite family of asymptotically‎ ‎nonexpansive in the intermediate sense and asymptotically‎ ‎quasi-pseudocontractive type mappings in normed linear spaces are‎ ‎established by using a new analytical method‎, ‎which essentially‎ ‎improve and extend some recent results obtained by yang‎ ‎...

Abstract In recent years, researchers have studied the use of different iteration processes from fixed point theory in generation complex fractals. For instance, Mann, Ishikawa, Noor, Jungck–Mann and Jungck–Ishikawa iterations been used. this paper, we study Picard–Mann with s -convexity Mandelbrot Julia sets. We prove escape criterion for $$(k+1)$$ <mml:math xmlns:mml="http://www.w3.org/1998/M...

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 ...