scholarly journals STRONG CONVERGENCE THEOREMS FOR COMMUTATIVE NONEXPANSIVE SEMIGROUPS IN GENERAL BANACH SPACES

2005 ◽  
Vol 9 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Hiromichi Miyake ◽  
Wataru Takahashi
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Convergence Theorems ◽  
Nonexpansive Semigroups

scholarly journals Convergence Theorems of a General Composite Iterative Method for Nonexpansive Semigroups in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-24 ◽  
Author(s):  
Pitipong Sunthrayuth ◽  
Kriengsak Wattanawitoon ◽  
Poom Kumam
Keyword(s):  
Iterative Method ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Iterative Scheme ◽  
Iteration Scheme ◽  
Convergence Theorems ◽  
Nonexpansive Semigroups

We introduce a general composite iterative scheme for nonexpansive semigroups in Banach spaces. We establish some strong convergence theorems of the general iteration scheme under different control conditions. The results presented in this paper improve and extend the corresponding results of Marino and Xu (2006), and others, from Hilbert spaces to Banach spaces.

scholarly journals An iterative process for a hybrid pair of generalized I-asymptotically nonexpansive single-valued mappings and generalized nonexpansive multi-valued mappings in Banach spaces

2018 ◽  
Vol 34 (1) ◽  
pp. 31-45
Author(s):  
ALI FARAJZADEH ◽  
◽  
PREEYANUCH CHUASUK ◽  
ANCHALEE KAEWCHAROEN ◽  
MOHAMMAD MURSALEEN ◽  
...  
Keyword(s):  
Weak Convergence ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Iterative Process ◽  
Finite Family ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive ◽  
Hybrid Pair

In this paper, an iterative process for a hybrid pair of a finite family of generalized I-asymptotically nonexpansive single-valued mappings and a finite family of generalized nonexpansive multi-valued mappings is established. Moreover, the weak convergence theorems and strong convergence theorems of the proposed iterative process in Banach spaces are proven. The examples are established for supporting our main results. The obtained results can be viewed as an improvement and extension of the several results in the literature.

Sign in / Sign up

Export Citation Format

Share Document