A COMPOSITE EXPLICIT ITERATIVE PROCESS WITH A VISCOSITY METHOD FOR LIPSCHITZIAN SEMIGROUP IN A SMOOTH BANACH SPACE

作者：Katchang P; Kumam P^*

来源：Bulletin of the Iranian Mathematical Society, 2011, 37(1): 143-159.

• Nonexpansive mapping
• fixed point
• amenable semigroup
• iteration
• left reversible

We introduce a new explicit composite iteration scheme with a viscosity iteration method for approximating a common fixed point of Lipschitzian semigroup on a compact convex subset of a smooth Banach space. We show that the iterative sequence converges strongly to a common fixed point under some parameter controlling conditions. Our results extend and improve the recent results by Saeidi [S. Saeidi, Fixed Point Theory Appl. (2008) Art. ID 363257 17pp.], Zhang et al. [S.-S. Zhang, L. Yang and J.-A. Liu, Appl. Math. Mech. (English Ed.) 28 (2007) 1287-1297.] and several others.

• 出版日期2011-4