VISCOSITY APPROXIMATION METHODS OF AVERAGING ITERATION FOR NONEXPANSIVE NONSELF-MAPPINGS

Lin-Fang Xing (P. R. China) and Rudong Chen (P. R. China)

Received February 17, 2007

References:

[1] J. S. Jung, Iterative approachs to common fixed points of nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 302 (2005), 509-520. [2] S. Matsushita and D. Kuroiwa, Strong convergence of averaging iterations of nonexpansive mappings, J. Math. Anal. Appl. 294 (2004), 206-214. [3] Y. S. Song and R. D. Chen, Viscosity approximation methods for nonexpansive nonself-mappings, J. Math. Anal. Appl. 321 (2006), 316-326. [4] Wataru Takahashi, Nonlinear functional analysis, Fixed Point Theory and its Applications, Yokohama Publishers, Inc., 2000. [5] W. Takahashi and G.-E. Kim, Strong convergence of approximants to fixed points of nonexpansive nonself-mappings in Banach spaces, Nonlinear Anal. 32 (1998), 447-454. [6] H.-K. Xu, Approximating curves of nonexpansive nonself mappings in Banach spaces, Mathematical Analysis, C. R. Acad. Sci. Paris 325 (1997), 151-156. [7] H.-K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl. 298 (2004), 279-291.

Keywords and phrases: strong convergence, nonexpansive nonself-mapping, weakly inward condition.