| MSC: | 46C05 | Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) |
| 47D03 | Groups and semigroups of linear operators {For nonlinear operators, see 47H20; see also 20M20} | |
| 47H09 | Nonexpansive mappings, and their generalizations (ultimately compact mappings, measures of noncompactness and condensing mappings, $A$-proper mappings, $K$-set contractions, etc.) |
|
| 47H10 | Fixed-point theorems [See also 54H25, 55M20, 58C30] | |
| 47H20 | Semigroups of nonlinear operators | |
| ZDM: | - | |
| CR: | - | |
| PACS: | - |
Abstract:
In this paper, we introduce the iterative sequence for two
asymptotically nonexpansive mappings and two asymptotically nonexpansive
semigroups. Then we prove strong convergence theorems for a common
fixed point of two asymptotically nonexpansive mappings and for a
common fixed point of two asymptotically nonexpansive semigroups by
using the new hybrid methods in a Hilbert space. Moreover, we
discuss the problem of strong convergence and we also apply our
results to generalizes extend and improve these announced by
Plubtieng and Ungchittrakool's result [Strong convergence of
modified Ishikawa iterations for two asymptotically nonexpansive
mappings and semigroups, Nonlinear Anal. 67 (2007) 2306--2315.] and
Takahashi et al. [Strong convergence theorems by hybrid methods for
families of nonexpansive mappings in Hilbert spaces, J.\ Math.\ Anal.\
Appl.\ 341 (2008) 276--286.].