SILPAKORN UNIVERSITY SCIENCE AND TECHNOLOGY JOURNAL, Vol 2, No 1 (2008)

Convergence of Three- Step Mean Value Iterative Scheme for a Mapping of Asymptotically Quasi – Nonexpansive Type

Narongrit Puturong

Mathematics Program, Faculty of Science Udonthani Rajabhat University


Abstract


In this paper, convergences of three- step mean value iterative scheme are established for a mapping of asymptotically quasi – nonexpansive type in a uniformly convex Banach space. The results obtained in this paper extend and improve the recent ones announced by D. R. Sahu and J. S. Jung [ Sahu and Jung, (2003) Fixed – point iteration processes for non- Lipschitzian mappings of asymptotically quasi- nonexpansive type, International Journal of Mathematics and Mathematical Sciences 2003 : 2075 - 2081], and many others.

Key Words: Asymptotically quasi – nonexpansive type; Completely continuous; Uniformly convex Banach space; Three – step mean value iterative scheme

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