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General iterative method for solving fixed point problems involving a finite family of demicontractive mappings in Banach spaces

Sow Thierno M. M.

Commentationes Mathematicae

2019

Vol. 59, No. 1/2

63--80

The purpose of this paper is to study the general iterative method for demicontractive mappings in Banach spaces. The method gives us a strong convergence iteration for a finite family of demicontractive mappings and also permits us to solve variational inequality problems involving accretive operators without any compactness condition. Finally, we provide some applications, and an illustration of the proposed method is given in l4 spaces. Our results improve many recent results using the general iterative method for finding the fixed points of nonlinear operators.

Iterative construction of a common fixed point of finite families of nonlinear mappings

Ofoedu E. U., Shehu Y.

Journal of Applied Analysis

2010

Vol. 16, nr 1

59-77

Let K be a nonempty closed convex subset of a real reflexive Banach space E with uniformly Gâteuax differentiable norm. Let T1, T2, ..., Tm : K —> K be m Lipschitz mappings (for some m ∈ N) such that (wzór). We construct a new iteration process and prove that the iteration process converges strongly to a common fixed point of these mappings provided at least one of the mappings is pseudocontractive. We also obtain as easy corollaries convergence results for finite families of Lipschitz pseudocontractive mappings and nonexpansive mappings. Furthermore, We prove that a slight modification of our iteration process converges strongly to a common zero of a finite family of Lipschitz accretive operators. Our new iteration process and our method of proof are of independent interest.