CONVERGENCE THEOREMS ON VISCOSITY APPROXIMATION METHODS FOR FINITE NONEXPANSIVE MAPPINGS IN BANACH SPACES

Jung, Jong-Soo; Jung, Jong-Soo

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E-ISSN2287-6081
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Vol.16 No.1

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CONVERGENCE THEOREMS ON VISCOSITY APPROXIMATION METHODS FOR FINITE NONEXPANSIVE MAPPINGS IN BANACH SPACES

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2009, v.16 no.1, pp.85-98

Jung, Jong-Soo

Jung,, J. (2009). CONVERGENCE THEOREMS ON VISCOSITY APPROXIMATION METHODS FOR FINITE NONEXPANSIVE MAPPINGS IN BANACH SPACES. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 16(1), 85-98.

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Abstract

Strong convergence theorems on viscosity approximation methods for finite nonexpansive mappings are established in Banach spaces. The main theorem generalize the corresponding result of Kim and Xu [10] to the viscosity approximation method for finite nonexpansive mappings in a reflexive Banach space having a uniformly Gateaux differentiable norm. Our results also improve the corresponding results of [7, 8, 19, 20].

keywords: Mann iteration, viscosity approximation method, nonexpansive mapping, common fixed points, contraction, uniformly Gateaux differentiable norm, variational inequality

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Article Contents

Vol.16 No.1

CONVERGENCE THEOREMS ON VISCOSITY APPROXIMATION METHODS FOR FINITE NONEXPANSIVE MAPPINGS IN BANACH SPACES

Abstract

Reference

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics