IJPAM: Volume 80, No. 1 (2012)

STRONG CONVERGENCE THEOREMS OF VISCOSITY
APPROXIMATION PROCESS FOR QUASI-NONEXPANSIVE
MAPPINGS IN HILBERT SPACES

Qiu-Mei Sun$^1$, Meng Li$^2$, Hai-Yun Zhou$^3$
$^{1,2,3}$Department of Mathematics
Journal of Ordnance
Engineering College
Shijiazhuang, 050003, P.R. CHINA


Abstract. In this paper, we have discussed the strong convergence of two modifications of the viscosity approximation method in Hilbert spaces, relatively to the computation of fixed points of operators in the class of quasi-nonexpansive mappings.

Our convergence theorems extend a recent result of P.E. Maingé, see [1].

Received: May 23, 2012

AMS Subject Classification: 47H05, 47H09, 49H17

Key Words and Phrases: Banach contraction, demiclosed, quasi-nonexpansive, variational inequality

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 80
Issue: 1