Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2013, Special Issue (2012), Article ID 904164, 10 pages.
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 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.
Abstr. Appl. Anal., Volume 2013, Special Issue (2012), Article ID 904164, 10 pages.
First available in Project Euclid: 26 February 2014
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Guu, Sy-Ming; Takahashi, Wataru. Existence and Approximation of Attractive Points of the Widely More Generalized Hybrid Mappings in Hilbert Spaces. Abstr. Appl. Anal. 2013, Special Issue (2012), Article ID 904164, 10 pages. doi:10.1155/2013/904164. https://projecteuclid.org/euclid.aaa/1393442736