• 대한수학회논문집
• /
• 제13권3호
• /
• pp.501-513
• /
• 1998

In this paper, we deal with the asymptotic behavior for the almost-orbits {u(t)} of an asymptotically nonexpansive semigroup S = {S(t) : t $\in$ G} for a right reversible semitopological semigroup G, defined on a suitable subset C of Banach spaces with the Opial's condition, locally uniform Opial condition, or uniform Opial condition.

• 대한수학회논문집
• /
• 제12권2호
• /
• pp.237-250
• /
• 1997

In this paper, we study the asymptotic behavior of orbits ${S(t)x}$ of an asymptotically nonexpansive semigroup $S = {S(t) : t \in G}$ for a right reversible semitopological semigroup G, defined on a weakly compact convex subset C of Banach spaces with Opial's condition for any $x \in C$.

• 대한수학회보
• /
• 제50권3호
• /
• pp.1007-1020
• /
• 2013

Approximate fixed point property problem for Mann iteration sequence of a nonexpansive mapping has been resolved on a Banach space independent of uniform (strict) convexity by Ishikawa [Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 59 (1976), 65-71]. In this paper, we solve this problem for a class of mappings wider than the class of asymptotically nonexpansive mappings on an arbitrary normed space. Our results generalize and extend several known results.