Iterative Algorithms for a System of Variational Inclusions Involving Set-Valued Quasi-Contractive Mappings in Banach Spaces

2021 ◽  
pp. 1-18
Author(s):  
Yangqing Qiu ◽  
Xiaomei Liu
Keyword(s):  
Banach Spaces ◽  
Iterative Algorithms ◽  
Variational Inclusions ◽  
Contractive Mappings

scholarly journals Iterative Algorithms for a System of Variational Inclusions in Banach Spaces

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 811 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Mihai Postolache ◽  
Yonghong Yao
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Iterative Procedure ◽  
Iterative Algorithms ◽  
Variational Inclusions

A system of variational inclusions (GSVI) is considered in Banach spaces. An implicit iterative procedure is proposed for solving the GSVI. Strong convergence of the proposed algorithm is given.

scholarly journals Iterative methods for generalized split feasibility problems in Banach spaces

2017 ◽  
Vol 33 (1) ◽  
pp. 09-26
Author(s):  
QAMRUL HASAN ANSARI ◽  
◽  
AISHA REHAN ◽  
◽  
Keyword(s):  
Weak Convergence ◽  
Banach Spaces ◽  
Iterative Methods ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Algorithms ◽  
Approximate Solutions ◽  
Split Feasibility Problems ◽  
Convergence Results ◽  
Split Feasibility

Inspired by the recent work of Takahashi et al. [W. Takahashi, H.-K. Xu and J.-C. Yao, Iterative methods for generalized split feasibility problems in Hilbert spaces, Set-Valued Var. Anal., 23 (2015), 205–221], in this paper, we study generalized split feasibility problems (GSFPs) in the setting of Banach spaces. We propose iterative algorithms to compute the approximate solutions of such problems. The weak convergence of the sequence generated by the proposed algorithms is studied. As applications, we derive some algorithms and convergence results for some problems from nonlinear analysis, namely, split feasibility problems, equilibrium problems, etc. Our results generalize several known results in the literature including the results of Takahashi et al. [W. Takahashi, H.-K. Xu and J.-C. Yao, Iterative methods for generalized split feasibility problems in Hilbert spaces, SetValued Var. Anal., 23 (2015), 205–221].

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