Convergence Theorems for Maximal Monotone Operators, Weak Relatively Nonexpansive Mappings and Equilibrium Problems
نویسندگان
چکیده
منابع مشابه
Convergence Theorems for Maximal Monotone Operators, Weak Relatively Nonexpansive Mappings and Equilibrium Problems
We introduce hybrid-iterative schemes for solving a system of the zero-finding problems of maximal monotone operators, the equilibrium problem, and the fixed point problem of weak relatively nonexpansive mappings. We then prove, in a uniformly smooth and uniformly convex Banach space, strong convergence theorems by using a shrinking projection method. We finally apply the obtained results to a ...
متن کاملHybrid Proximal-Type Algorithms for Generalized Equilibrium Problems, Maximal Monotone Operators, and Relatively Nonexpansive Mappings
The purpose of this paper is to introduce and consider new hybrid proximal-type algorithms for finding a common element of the set EP of solutions of a generalized equilibrium problem, the set F S of fixed points of a relatively nonexpansive mapping S, and the set T−10 of zeros of a maximal monotone operator T in a uniformly smooth and uniformly convex Banach space. Strong convergence theorems ...
متن کاملStrong convergence theorems for equilibrium problems and weak Bregman relatively nonexpansive mappings in Banach spaces
In this paper, a shrinking projection algorithm based on the prediction correction method for equilibrium problems and weak Bregman relatively nonexpansive mappings is introduced and investigated in Banach spaces, and then the strong convergence of the sequence generated by the proposed algorithm is derived under some suitable assumptions. These results are new and develop some recent results i...
متن کاملConvergence Theorems for Two Families of Weak Relatively Nonexpansive Mappings and a Family of Equilibrium Problems
The purpose of this paper is to prove strong convergence theorems for common fixed points of two families of weak relatively nonexpansive mappings and a family of equilibrium problems by a new monotone hybrid method in Banach spaces. Because the hybrid method presented in this paper is monotone, so that the method of the proof is different from the original one. We shall give an example which i...
متن کاملMonotone Cq Algorithm for Weak Relatively Nonexpansive Mappings and Maximal Monotone Operators in Banach Spaces
The purpose of this article is to prove strong convergence theorems for weak relatively nonexpansive mapping which is firstly presented in this article. In order to get the strong convergence theorems for weak relatively nonexpansive mapping, the monotone CQ iteration method is presented and is used to approximate the fixed point of weak relatively nonexpansive mapping, therefore this article a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Applied Mathematics
سال: 2012
ISSN: 1110-757X,1687-0042
DOI: 10.1155/2012/804538