Strong Convergence Theorems by Generalized Cq Method in Hilbert Spaces
نویسندگان
چکیده
Recently, CQ method has been investigated extensively. However, it is mainly applied to modify Mann, Ishikawa and Halpern iterations to get strong convergence. In this paper, we study the properties of CQ method and proposed a framework. Based on that, we obtain a series of strong convergence theorems. Some of them are the extensions of previous results. On the other hand, CQ method, monotone Q method, monotone C method and monotone CQ method, used to be given separately, have the following relations: CQ method TRUE ⇒ monotone Q method TRUE ⇒ monotone C method TRUE ⇔ monotone CQ method TRUE.
منابع مشابه
Approximating Fixed Points of 2-generalized Hybrid Mappings in Banach Spaces and Cat(0) Spaces
In this paper, we first prove weak and strong convergence theorems for Ishikawa and Halpern iterations of 2-generalized hybrid mappings in uniformly convex Banach spaces and we apply our method to provide an affirmative answer to an open problem raised by Hojo, Takahashi and Termwuttipong [Strong convergence theorems for 2-generalized hybrid mappings in Hilbert spaces, Nonlinear Analysis, 75 (2...
متن کاملA Generalized System of Nonlinear Variational Inequalities in Hilbert Spaces
In this paper, we consider convergence of iterative-projection method for solutions of a generalized system for three different nonlinear relaxed co-coercive mappings in the framework of Hilbert spaces. Strong convergence theorems are established. Our results improve and extend the recent ones announced by many others. AMS (MOS) Subject Classification Codes: 47H05, 47H09, 47J25
متن کاملConvergence theorems of multi-step iterative algorithm with errors for generalized asymptotically quasi-nonexpansive mappings in Banach spaces
The purpose of this paper is to study and give the necessary andsufficient condition of strong convergence of the multi-step iterative algorithmwith errors for a finite family of generalized asymptotically quasi-nonexpansivemappings to converge to common fixed points in Banach spaces. Our resultsextend and improve some recent results in the literature (see, e.g. [2, 3, 5, 6, 7, 8,11, 14, 19]).
متن کاملWeak and Strong Convergence Theorems for Generalized Hybrid Mappings in Hilbert Spaces
In this paper, we first obtain a weak mean convergence theorem of Baillon’s type for generalized hybrid mappings in a Hilbert space. Further, using an idea of mean convergence, we prove a strong convergence theorem of Halpern’s type for generalized hybrid mappings in a Hilbert space.
متن کاملWeak convergence theorems for symmetric generalized hybrid mappings in uniformly convex Banach spaces
In this paper, we prove some theorems related to properties of generalized symmetric hybrid mappings in Banach spaces. Using Banach limits, we prove a fixed point theorem for symmetric generalized hybrid mappings in Banach spaces. Moreover, we prove some weak convergence theorems for such mappings by using Ishikawa iteration method in a uniformly convex Banach space.
متن کامل