Strong convergence of the Halpern subgradient extragradient method for solving variational inequalities in Banach spaces
نویسندگان
چکیده
منابع مشابه
Strong Convergence of the Halpern Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Spaces
In this paper, we combine the subgradient extragradient method with the Halpern method for finding a solution of a variational inequality involving a monotone Lipschitz mapping in Banach spaces. By using the generalized projection operator and the Lyapunov functional introduced by Alber, we prove a strong convergence theorem. We also consider the problem of finding a common element of the set o...
متن کاملA modified subgradient extragradient method for solving monotone variational inequalities
In the setting of Hilbert space, a modified subgradient extragradient method is proposed for solving Lipschitz-continuous and monotone variational inequalities defined on a level set of a convex function. Our iterative process is relaxed and self-adaptive, that is, in each iteration, calculating two metric projections onto some half-spaces containing the domain is involved only and the step siz...
متن کاملModified Noor’s Extragradient Method for Solving Generalized Variational Inequalities in Banach Spaces
and Applied Analysis 3 2. Preliminaries Let C be a nonempty closed convex subset of a real Banach space E. Recall that a mapping A of C into E is said to be accretive if there exists j x − y ∈ J x − y such that 〈 Ax −Ay, j(x − y)〉 ≥ 0, 2.1 for all x, y ∈ C. A mapping A of C into E is said to be α-strongly accretive if, for α > 0, 〈 Ax −Ay, j(x − y)〉 ≥ α∥∥x − y∥∥2, 2.2 for all x, y ∈ C. A mappin...
متن کاملThe Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space
We present a subgradient extragradient method for solving variational inequalities in Hilbert space. In addition, we propose a modified version of our algorithm that finds a solution of a variational inequality which is also a fixed point of a given nonexpansive mapping. We establish weak convergence theorems for both algorithms.
متن کاملStrong convergence for variational inequalities and equilibrium problems and representations
We introduce an implicit method for nding a common element of the set of solutions of systems of equilibrium problems and the set of common xed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. Then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition for ...
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: The Journal of Nonlinear Sciences and Applications
سال: 2017
ISSN: 2008-1898,2008-1901
DOI: 10.22436/jnsa.010.02.06