Communications of the Korean Mathematical Society (대한수학회논문집)
- Volume 11 Issue 1
- /
- Pages.71-79
- /
- 1996
- /
- 1225-1763(pISSN)
- /
- 2234-3024(eISSN)
Strong convergence theorems for nonexpansive mappings in banach spaces
-
Park, Jong-Yeoul
(Department of Mathematics, Pusan National University)
;
-
Jung, Jong-Soo
(Department of Mathematics, Dong-A University)
;
- Jeong, Jae-Ug (Department of Mathematics, Dongeui University)
- Published : 1996.01.01
Abstract
In this paper, we prove for a nonexpansive mapping T that under certain conditions the trajectory $t \to G_t(x), t \in [0,1]$, defined by the equation $G_t(x) = (1 - t)x + tTG_t(x)$ strongly converges to a fixed point of T as $t \to 1^{-1}$.