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1

Approximation of common fixed points of left Bregman strongly nonexpansive mappings and solutions of equilibrium problems

Shehu Y., Ogbuisi F. U.

Journal of Applied Analysis

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2015

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Vol. 21, nr 2

63--77

EN

In this paper we propose an iterative algorithm based on the hybrid method in mathematical programming for approximating a common fixed point of an infinite family of left Bregman strongly nonexpansive mappings which also solves a finite system of equilibrium problems in a reflexive real Banach space.We further prove that our iterative sequence converges strongly to a common fixed point of an infinite family of left Bregman strongly nonexpansive mappings which is also a common solution to a finite system of equilibrium problems. Our result extends many recent and important results in the literature.

2

Strong convergence theorems for the approximation of fixed points of demicontinuous pseudocontractive mappings

Chidume C. E, Shehu Y.

Journal of Applied Analysis

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2013

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Vol. 19, nr 2

213--229

EN

In this paper, we introduce a new explicit iterative scheme for approximation of fixed points of demicontinuous pseudocontractive mappings in uniformly smooth Banach spaces and prove strong convergence of our proposed iterative scheme. Furthermore, we modify our explicit iterative scheme for approximation of zeroes of bounded demicontinuous accretive mappings in uniformly smooth Banach spaces. Our result improves, extends and unifies most of the results that have been proved for this class of mappings.

3

Strong convergence theorems for relatively quasi-nonexpansive mappings, variational inequality problems and systems of generalized mixed equilibrium problems

Shehu Y., Oguguo O.

Journal of Applied Analysis

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2012

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Vol. 18, nr 1

69-95

EN

In this paper, we construct a new iterative scheme by hybrid methods to approximate a common element in the fixed points set of an infinite family of relatively quasi-nonexpansive mappings, the solutions set of a variational inequality problem and the solutions set of a system of generalized mixed equilibrium problems in a 2-uniformly convex real Banach space which is also uniformly smooth. Then, we prove strong convergence of the scheme to a common element of the three sets. We give several applications of our results in a Banach space. Our results extend many known recent results in the literature.

4

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

Ofoedu E. U., Shehu Y.

Journal of Applied Analysis

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2010

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Vol. 16, nr 1

59-77

EN

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.