Strong convergence studied by a hybrid type method for monotone operators in a Banach space

DOI10.1016/j.na.2007.04.010zbMath1220.47095OpenAlexW2015322583MaRDI QIDQ927936

Hideaki Iiduka, Takahashi, Wataru

Publication date: 10 June 2008

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2007.04.010

zbMATH Keywords

strong convergencevariational inequality problemgeneralized projectionzero pointinverse-strongly monotone operator\(p\)-uniformly convex

Mathematics Subject Classification ID

Monotone operators and generalizations (47H05) Iterative procedures involving nonlinear operators (47J25) Equations involving nonlinear operators (general) (47J05)

Related Items

Strong convergence theorem for relatively nonexpansive mapping and inverse-strongly-monotone mapping in a Banach space ⋮ Mann-Type Steepest-Descent and Modified Hybrid Steepest-Descent Methods for Variational Inequalities in Banach Spaces ⋮ Forcing strong convergence of Korpelevich's method in Banach spaces with its applications in game theory ⋮ A hybrid iteration scheme for equilibrium problems, variational inequality problems and common fixed point problems in Banach spaces ⋮ Convergence theorems for common solutions of various problems with nonlinear mapping ⋮ A hybrid scheme for finite families of equilibrium, variational inequality and fixed point problems ⋮ Strong convergence theorems for a common point of solution of variational inequality, solutions of equilibrium and fixed point problems ⋮ A hybrid approximation method for equilibrium, variational inequality and fixed point problems ⋮ Weak convergence of an iterative sequence for accretive operators in Banach spaces ⋮ New algorithms for approximating zeros of inverse strongly monotone maps and \(J\)-fixed points ⋮ Strong convergence theorem for total quasi-\(\phi\)-asymptotically nonexpansive mappings in a Banach space ⋮ Convergence results for a common solution of a finite family of variational inequality problems for monotone mappings with Bregman distance function ⋮ Strong convergence theorems for variational inequality problems and quasi-\(\phi\)-asymptotically nonexpansive mappings ⋮ Approximating common solution of variational inequality problems for two monotone mappings in Banach spaces ⋮ Strong convergence theorems for fixed point problems, variational inequality problems and system of generalized mixed equilibrium problems ⋮ \(J\)-variational inequalities and zeroes of a family of maximal monotone operators by sunny generalized nonexpansive retraction ⋮ Strong convergence theorems for a solution of finite families of equilibrium and variational inequality problems ⋮ Combination of the hybrid steepest-descent method and the viscosity approximation ⋮ An iteration to a common point of solution of variational inequality and fixed point-problems in Banach spaces ⋮ Strong Convergence of an Inexact Proximal Point Algorithm for Equilibrium Problems in Banach Spaces ⋮ Strong convergence theorems for monotone mappings and relatively weak nonexpansive mappings ⋮ Strong convergence theorems for relatively nonexpansive mappings and Lipschitz-continuous monotone mappings in Banach spaces ⋮ Minimum-norm solution of variational inequality and fixed point problem in banach spaces ⋮ Convergence theorems of common solutions for fixed point, variational inequality and equilibrium problems ⋮ Strong convergence to a solution of a variational inequality problem in Banach spaces ⋮ Weak convergence of a hybrid type method with errors for a maximal monotone mapping in Banach spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quelques propriétés des opérateurs angle-bornes et n-cycliquement monotones
• Regularization of nonlinear ill-posed variational inequalities and convergence rates
• Sharp uniform convexity and smoothness inequalities for trace norms
• Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups.
• Forcing strong convergence of proximal point iterations in a Hilbert space
• Construction of fixed points of nonlinear mappings in Hilbert space
• Inequalities in Banach spaces with applications
• Monotone Operators and the Proximal Point Algorithm
• Strong Convergence of a Proximal-Type Algorithm in a Banach Space
• Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications
• Variational inequalities
• On the Maximality of Sums of Nonlinear Monotone Operators
• On uniformly convex functions