Viscosity approximation methods for W-mappings in Hilbert space
Authors
Abstract:
We suggest a explicit viscosity iterative algorithm for nding a common elementof the set of common xed points for W-mappings which solves somevariational inequality. Also, we prove a strong convergence theorem with somecontrol conditions. Finally, we apply our results to solve the equilibrium problems.Finally, examples and numerical results are also given.
similar resources
Viscosity Approximation Methods for Nonexpansive Nonself-Mappings in Hilbert Spaces
Viscosity approximation methods for nonexpansive nonself-mappings are studied. Let C be a nonempty closed convex subset of Hilbert space H , P a metric projection of H onto C and let T be a nonexpansive nonself-mapping from C into H . For a contraction f on C and {tn} ⊆ (0,1), let xn be the unique fixed point of the contraction x → tn f (x) + (1− tn)(1/n) ∑n j=1(PT) x. Consider also the iterati...
full textGeneralized viscosity approximation methods for nonexpansive mappings
We combine a sequence of contractive mappings {fn} and propose a generalized viscosity approximation method. One side, we consider a nonexpansive mapping S with the nonempty fixed point set defined on a nonempty closed convex subset C of a real Hilbert space H and design a new iterative method to approximate some fixed point of S, which is also a unique solution of the variational inequality. O...
full textViscosity Approximation Methods for Strict Pseudo-Contractive Nonself-Mappings in Hilbert Spaces
In this paper, we introduce a new iterative scheme by viscosity approximation methods for strict pseudo-contractive nonself-mappings in Hilbert spaces and obtain a strong convergence theorem. The theorem improves and extends the result of Shimizu and Takahashi [T. Shimizu, W. Takahashi, Strong convergence to common fixed points of families of nonexpansive mappings, J. Math. Anal. Appl. 211 (199...
full textViscosity approximation methods for pseudocontractive mappings in Banach spaces
Strong convergence of implicit viscosity approximation methods for pseudocontractive mappings in Banach spaces Lu-Chuan Ceng a b , Adrian Petruşel c , Mu-Ming Wong d & Su-Jane Yu e a Department of Mathematics, Shanghai Normal University, Shanghai 200234, China b Scientific Computing Key Laboratory of Shanghai Universities, Shanghai, China c Department of Applied Mathematics, Babeş-Bolyai Univer...
full textViscosity approximation methods for nonexpansive mappings in CAT(0) spaces
The purpose of this paper is to study the strong convergence theorems of Moudafi's viscosity approximation methods for a nonexpansive mapping T in CAT(0) spaces without the property P. For a contraction f on C and t ∈ (0, 1), let x t ∈ C be the unique fixed point of the contraction x → tf (x) ⊕ (1 – t)Tx; i.e., x t = tf (x t) ⊕ (1 – t)Tx t and x n+1 = α n f (x n) ⊕ (1 – α n)Tx n , n ≥ 0, where ...
full textViscosity Approximation Methods for Fixed Points of Asymptotically Nonexpansive Mappings in Banach Space
In this paper, under the framework of Banach space with uniformly Gateaux differentiable norm and uniform normal structure, we use the existence theorem of fixed points of Li and Sims to investigate the convergence of the implicit iteration process and the explicit iteration process for asymptotically nonexpansive mappings. We get the convergence theorems.
full textMy Resources
Journal title
volume 11 issue 2
pages 15- 35
publication date 2017-06-01
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023