Fixed point theorems for nonlinear non-self mappings in Hilbert spaces and applications

被引：4
作者：
Takahashi, Wataru [1 ,2 ]
Wong, Ngai-Ching [2 ,3 ]
Yao, Jen-Chih [3 ,4 ]
机构：
[1] Tokyo Inst Technol, Dept Math & Comp Sci, Tokyo 1528552, Japan
[2] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 80424, Taiwan
[3] Kaohsiung Med Univ, Ctr Fundamental Sci, Kaohsiung 80702, Taiwan
[4] King Abdulaziz Univ, Dept Math, Jeddah 21589, Saudi Arabia
来源：
FIXED POINT THEORY AND APPLICATIONS | 2013年
基金：
日本学术振兴会;
关键词：
Hilbert space; nonexpansive mapping; nonspreading mapping; hybrid mapping; fixed point; non-self mapping; GENERALIZED HYBRID MAPPINGS; STRONG-CONVERGENCE THEOREMS; ERGODIC-THEOREMS; WEAK; APPROXIMATION; EXISTENCE;
D O I：
10.1186/1687-1812-2013-116
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Recently, Kawasaki and Takahashi (J. Nonlinear Convex Anal. 14:71-87, 2013) defined a broad class of nonlinear mappings, called widely more generalized hybrid, in a Hilbert space which contains generalized hybrid mappings (Kocourek et al. in Taiwan. J. Math. 14:2497-2511, 2010) and strict pseudo-contractive mappings (Browder and Petryshyn in J. Math. Anal. Appl. 20:197-228, 1967). They proved fixed point theorems for such mappings. In this paper, we prove fixed point theorems for widely more generalized hybrid non-self mappings in a Hilbert space by using the idea of Hojo et al. (Fixed Point Theory 12:113-126, 2011) and Kawasaki and Takahashi fixed point theorems (J. Nonlinear Convex Anal. 14: 71-87, 2013). Using these fixed point theorems for non-self mappings, we proved the Browder and Petryshyn fixed point theorem (J. Math. Anal. Appl. 20: 197-228, 1967) for strict pseudo-contractive non-self mappings and the Kocourek et al. fixed point theorem (Taiwan. J. Math. 14: 2497-2511, 2010) for super hybrid non-self mappings. In particular, we solve a fixed point problem.
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页数：14
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