scholarly journals An Inexact Proximal-Type Method for the Generalized Variational Inequality in Banach Spaces

2007 ◽  
Vol 2007 (1) ◽  
pp. 078124
Author(s):  
LC Ceng ◽  
G Mastroeni ◽  
JC Yao
Keyword(s):  
Variational Inequality ◽  
Banach Spaces ◽  
Type Method ◽  
Generalized Variational Inequality ◽  
Inexact Proximal

scholarly journals A New Algorithm for the Common Solutions of a Generalized Variational Inequality System and a Nonlinear Operator Equation in Banach Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1944
Author(s):  
Yuanheng Wang ◽  
Cancan Li ◽  
Lirong Lu
Keyword(s):  
Variational Inequality ◽  
Banach Spaces ◽  
Optimization Problem ◽  
Nonlinear Operator ◽  
Iterative Scheme ◽  
Nonlinear Operator Equation ◽  
Convex Optimization Problem ◽  
Generalized Variational Inequality ◽  
Inequality System ◽  
The Common

We study a new algorithm for the common solutions of a generalized variational inequality system and the fixed points of an asymptotically non-expansive mapping in Banach spaces. Under some specific assumptions imposed on the control parameters, some strong convergence theorems for the sequence generated by our new viscosity iterative scheme to approximate their common solutions are proved. As an application of our main results, we solve the standard constrained convex optimization problem. The results here generalize and improve some other authors’ recently corresponding results.

scholarly journals Extending the Applicability of a Two-Step Chord-Type Method for Non-Differentiable Operators

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 804
Author(s):  
Ioannis K. Argyros ◽  
Neha Gupta ◽  
J. P. Jaiswal
Keyword(s):  
Approximate Solution ◽  
Convergence Analysis ◽  
Banach Spaces ◽  
Recurrence Relation ◽  
Convergence Theorem ◽  
Local Convergence ◽  
Existence And Uniqueness ◽  
Numerical Illustration ◽  
Type Method ◽  
Local Convergence Analysis

The semi-local convergence analysis of a well defined and efficient two-step Chord-type method in Banach spaces is presented in this study. The recurrence relation technique is used under some weak assumptions. The pertinency of the assumed method is extended for nonlinear non-differentiable operators. The convergence theorem is also established to show the existence and uniqueness of the approximate solution. A numerical illustration is quoted to certify the theoretical part which shows that earlier studies fail if the function is non-differentiable.

scholarly journals An Iterative Algorithm for Solving Generalized Variational Inequalities and Fixed Points Problems

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 61 ◽  
Author(s):  
Yonghong Yao ◽  
Mihai Postolache ◽  
Jen-Chih Yao
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Fixed Points ◽  
Iterative Algorithm ◽  
Nonlinear Transformation ◽  
Generalized Variational Inequalities ◽  
Generalized Variational Inequality ◽  
Suggested Algorithm

In this paper, a generalized variational inequality and fixed points problem is presented. An iterative algorithm is introduced for finding a solution of the generalized variational inequalities and fixed point of two quasi-pseudocontractive operators under a nonlinear transformation. Strong convergence of the suggested algorithm is demonstrated.

Global weighted Orlicz estimates for irregular obstacle problems with general growth over bounded nonsmooth domains

2018 ◽  
Vol 20 (08) ◽  
pp. 1750083
Author(s):  
Yumi Cho
Keyword(s):  
Variational Inequality ◽  
Sobolev Spaces ◽  
Obstacle Problem ◽  
Obstacle Problems ◽  
Generalized Variational Inequality ◽  
Nonsmooth Domain ◽  
General Growth ◽  
Nonsmooth Domains

We study a generalized variational inequality with an irregular obstacle in the frame of Orlicz–Sobolev spaces. Over a bounded nonsmooth domain having a sufficiently flat boundary in the Reifenberg sense, a global weighted Orlicz estimate is established for the gradient of the solution to the obstacle problem assumed BMO smallness of a coefficient.

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