Abstract and Applied Analysis

Existence and Approximation of Attractive Points of the Widely More Generalized Hybrid Mappings in Hilbert Spaces

Sy-Ming Guu and Wataru Takahashi

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2012), Article ID 904164, 10 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393442736

Digital Object Identifier
doi:10.1155/2013/904164

Mathematical Reviews number (MathSciNet)
MR3073499

Zentralblatt MATH identifier
07095477

Citation

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


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