General implicit variational inclusion problems based on \(A\)-maximal (\(m\))-relaxed monotonicity (AMRM) frameworks

DOI10.1016/j.amc.2009.04.078zbMath1178.65073OpenAlexW2027851432MaRDI QIDQ732497

Ravi P. Agarwal, Ram U. Verma

Publication date: 9 October 2009

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2009.04.078

zbMATH Keywords

algorithmsvariational inequalityHilbert spacemaximal monotone mappingvariational inclusionsvariational graphical convergencegeneralized resolvent operator\(A\)-maximal \((m)\)-relaxed monotone mapping

Mathematics Subject Classification ID

Variational inequalities (49J40) Numerical methods for variational inequalities and related problems (65K15)

Related Items (7)

Graph-convergent analysis of over-relaxed \((A, \eta, m)\)-proximal point iterative methods with errors for general nonlinear operator equations ⋮ Convergence analysis of new over-relaxed proximal point algorithm frameworks with errors and applications to general \( A\)-monotone nonlinear inclusion forms ⋮ Graphical approximation of common solutions to generalized nonlinear relaxed cocoercive operator equation systems with \((A, \eta)\)-accretive mappings ⋮ Sensitivity analysis for generalized nonlinear parametric \((A,\eta ,m)\)-maximal monotone operator inclusion systems with relaxed cocoercive type operators ⋮ New approximation-solvability of general nonlinear operator inclusion couples involving \((A, \eta , m)\)-resolvent operators and relaxed cocoercive type operators ⋮ Common solutions of equilibrium and fixed point problems ⋮ A new method for solving a system of generalized nonlinear variational inequalities in Banach spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On a new system of nonlinear \(A\)-monotone multivalued variational inclusions
• \(A\)-monotonicity and its role in nonlinear variational inclusions
• General system of \(A\)-monotone nonlinear variational inclusion problems with applications
• A general framework for the over-relaxed A-proximal point algorithm and applications to inclusion problems
• Composition duality and maximal monotonicity
• Mixed equilibrium problems: sensitivity analysis and algorithmic aspect.
• Mann and Ishikawa type perturbed iterative algorithms for generalized nonlinear implicit quasi-variational inclusions
• The primal Douglas-Rachford splitting algorithm for a class of monotone mappings with application to the traffic equilibrium problem
• Generalized over-relaxed proximal algorithm based ona-maximal monotonicity framework and applications to inclusion problems
• A-monotone nonlinear relaxed cocoercive variational inclusions
• Approximation solvability of a class of nonlinear set-valued variational inclusions involving \((A,\eta )\)-monotone mappings
• Sensitivity analysis for generalized strongly monotone variational inclusions based on the \((A,\eta )\)-resolvent operator technique
• A new system of variational inclusions with \((H,\eta)\)-monotone operators in Hilbert spaces
• General system of \((A,\eta )\)-monotone variational inclusion problems based on generalized hybrid iterative algorithm
• General projection systems and relaxed cocoercive nonlinear variational inequalities
• Monotone Operators and the Proximal Point Algorithm
• Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming
• A class of projection-contraction methods applied to monotone variational inequalities

This page was built for publication: General implicit variational inclusion problems based on \(A\)-maximal (\(m\))-relaxed monotonicity (AMRM) frameworks