STRONG CONVERGENCE OF ANITERATIVE METHOD FOR CONTINUOUS PSEUDOCONTRACTIVE MAPPINGS

Yisheng Song (P. R. China)

Received August 29, 2006

References:

[1] Shih-Sen Chang, Yeoi Je Cho and Haiyan Zhou, Iterative Methods of Nonlinear Operator Equations in Banach Spaces, Nova Science Publishers, Inc., Huntington, New York, USA, 2002. [2] Rudong Chen, Yisheng Song and Haiyun Zhou, Convergence theorems for implicit iteration process for a finite family of continuous pseudocontractive mappings, J. Math. Anal. Appl. 314 (2006), 701-709. [3] Klaus Deimling, Zero of accretive operators, Manuscripta Math. 13 (1974), 365-374. [4] J. Gao, Modulus of convexity in Banach spaces, Appl. Math. Letters 16 (2003), 273-278. [5] Claudio H. Morales and Jong Soo Jung, Convergence of paths form pseudo-contractive mappings in Banach spaces, Proc. Amer. Math. Soc. 128 (2000), 3411-3419. [6] S. Reich, An iterative procedure for constructing zeros of accretive sets in Banach spaces, Nonlinear Anal. 2 (1978), 85-92. [7] Wataru Takahashi, Nonlinear Functional Analysis _ Fixed Point Theory and its Applications, Yokohama Publishers, Inc., Yokohama, 2000 (in Japanese). [8] Hong-Kun Xu, An iterative approach to quadratic optimization, J. Optim. Theo. Appl. 116 (2003), 659-678. [9] H. K. Xu and R. G. Ori, An implicit iteration process for nonexpansive mappings, Numer. Func. Anal. Optim. 22 (2001), 767-773.

Keywords and phrases: pseudocontractive mapping, modified implicit iterations, strong convergence.