Existence and Approximation of Attractive Points of the Widely More Generalized Hybrid Mappings in Hilbert Spaces
We study the widely more generalized hybrid mappings which have been proposed to unify several well-known nonlinear mappings including the nonexpansive mappings, nonspreading mappings, hybrid mappings, and generalized hybrid mappings. Without the convexity assumption, we will establish the existence...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/904164 |
| Summary: | We study the widely more generalized hybrid mappings which have been proposed to unify several well-known nonlinear mappings including the nonexpansive mappings, nonspreading mappings, hybrid
mappings, and generalized hybrid mappings. Without the convexity assumption, we will establish the existence theorem and mean convergence theorem
for attractive point of the widely more generalized hybrid mappings in a Hilbert
space. Moreover, we prove a weak convergence theorem of Mann’s type and a
strong convergence theorem of Shimizu and Takahashi’s type for such a wide
class of nonlinear mappings in a Hilbert space. Our results can be viewed as a
generalization of Kocourek, Takahashi and Yao, and Hojo and Takahashi where
they studied the generalized hybrid mappings. |
|---|---|
| ISSN: | 1085-3375 1687-0409 |