Fixed point, convergence and nonlinear ergodic theorems for some semigroups in Hilbert spaces

被引：0
作者：
Hossein Piri
Bayaz Daraby
Asghar Rahimi
Mostafa Ghasemi
机构：
[1] University of Bonab,Department of Mathematics, Faculty of Basic Science
[2] University of Maragheh,Department of Mathematics
来源：
Journal of Fixed Point Theory and Applications | 2020年 / 22卷
关键词：
Convergence theorem; nonlinear ergodic theorem; banach limit; invariant mean; 47H05; 47H09; 47H20;
D O I：
暂无
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摘要：
In this paper, we first introduce some semigroups of mappings called quasi-nonexpansive, nonspreading, hybrid, TJ-1, TJ-2, and generalized hybrid semigroup. Then, using the theory of invariant means, we prove fixed point theorems, weak convergence theorem of Mann’s type and generalized nonlinear ergodic theorem for such semigroups in a Hilbert space. Furthermore, we prove a strong convergence theorem of Halpern’s type for the proposed semigroups in a Hilbert space. The results presented in this paper mainly extend and improved some well-known results in the literature.
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