Article
Licensed
Unlicensed
Requires Authentication
Strong convergence theorems for relatively quasi-nonexpansive mappings, variational inequality problems and systems of generalized mixed equilibrium problems
-
Yekini Shehu
and
O. Oguguo
Published/Copyright:
June 5, 2012
Abstract.
In this paper, we construct a new iterative scheme by hybrid methods to approximate a common element in the fixed points set of an infinite family of relatively quasi-nonexpansive mappings, the solutions set of a variational inequality problem and the solutions set of a system of generalized mixed equilibrium problems in a 2-uniformly convex real Banach space which is also uniformly smooth. Then, we prove strong convergence of the scheme to a common element of the three sets. We give several applications of our results in a Banach space. Our results extend many known recent results in the literature.
Keywords: Relatively quasi-nonexpansive mappings; generalized mixed equilibrium problems; variational inequality problem; hybrid method; Banach spaces
Received: 2010-12-13
Revised: 2011-04-04
Accepted: 2011-04-18
Published Online: 2012-06-05
Published in Print: 2012-06-01
© 2012 by Walter de Gruyter Berlin Boston
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- Masthead
- Regularity theory for superquadratic energy functionals related to nonlinear Hencky materials in three dimensions
- Common fixed points of nonexpansive mappings with applications to best and best simultaneous approximation
- Perturbations of the matrix logarithm
- Strong convergence theorems for relatively quasi-nonexpansive mappings, variational inequality problems and systems of generalized mixed equilibrium problems
- Results of Tadeusz Świa̧tkowski on algebraic sums of sets and their applications in the theory of subadditive functions
- The generalized Stokes theorem for ℝ-linear forms on Lie algebroids
- Certain classes of multivalent functions with negative coefficients involving the Hadamard product
- Projective coordinates and compactification in elliptic, parabolic and hyperbolic 2-D geometry
- Location of zeros of polynomials
Keywords for this article
Relatively quasi-nonexpansive mappings;
generalized mixed equilibrium problems;
variational inequality problem;
hybrid method;
Banach spaces
Articles in the same Issue
- Masthead
- Regularity theory for superquadratic energy functionals related to nonlinear Hencky materials in three dimensions
- Common fixed points of nonexpansive mappings with applications to best and best simultaneous approximation
- Perturbations of the matrix logarithm
- Strong convergence theorems for relatively quasi-nonexpansive mappings, variational inequality problems and systems of generalized mixed equilibrium problems
- Results of Tadeusz Świa̧tkowski on algebraic sums of sets and their applications in the theory of subadditive functions
- The generalized Stokes theorem for ℝ-linear forms on Lie algebroids
- Certain classes of multivalent functions with negative coefficients involving the Hadamard product
- Projective coordinates and compactification in elliptic, parabolic and hyperbolic 2-D geometry
- Location of zeros of polynomials
