On Holder continuity of approximate solutions to parametric equilibrium problems

被引：24

作者：

Anh, L. Q. ^{[2
]}

Khanh, P. Q. ^{[3
]}

Tam, T. N. ^{[1
]}

机构：

[1] Taydo Univ, Dept Math, Can Tho, Vietnam

[2] Cantho Univ, Teacher Coll, Dept Math, Can Tho, Vietnam

[3] Int Univ Hochiminh City, Dept Math, Ho Chi Minh City, Vietnam

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2012年 / 75卷 / 04期

关键词：

Holder continuity; Approximate solutions; Parametric equilibrium problems; Concavity; Constrained minimization; Variational inequalities; Fixed point problems; GENERALIZED MONOTONE BIFUNCTIONS; VARIATIONAL INCLUSION PROBLEMS; SOLUTION SETS; SENSITIVITY-ANALYSIS; METRIC-SPACES; SOLUTION MAPPINGS; SEMICONTINUITY; STABILITY; EXISTENCE;

D O I：

10.1016/j.na.2011.10.029

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish verifiable sufficient conditions for Holder continuity of approximate solutions to parametric equilibrium problems, when solutions may be not unique. Many examples are provided to illustrate the need of considering approximate solutions instead of exact solutions and the essentialness of the imposed assumptions. As applications, we derive this Holder continuity for constrained minimization, variational inequalities and fixed point problems. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：2293 / 2303

页数：11

共 33 条

[1] On the stability of the solution sets of general multivalued vector quasiequilibrium problems [J].

Anh, L. Q. ;

Khanh, P. Q. .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2007, 135 (02) :271-284

[2] On the Holder continuity of solutions to parametric multivalued vector equilibrium problems [J].

Anh, L. Q. ;

Khanh, P. Q. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 321 (01) :308-315

[3] Holder Continuity of the Unique Solution to Quasiequilibrium Problems in Metric Spaces [J].

Anh, L. Q. ;

Khanh, P. Q. .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2009, 141 (01) :37-54

[4] Various kinds of semicontinuity and the solution sets of parametric multivalued symmetric vector quasiequilibrium problems [J].

Anh, Lam Quoc ;

Khanh, Phan Quoc .

JOURNAL OF GLOBAL OPTIMIZATION, 2008, 41 (04) :539-558

[5] Semicontinuity of the approximate solution sets of multivalued quasiequilibrium problems [J].

Anh, Lam Quoc ;

Khanh, Phan Quoc .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2008, 29 (1-2) :24-42

[6] Uniqueness and Holder continuity of the solution to multivalued equilibrium problems in metric spaces [J].

Anh, Lam Quoc ;

Khanh, Phan Quoc .

JOURNAL OF GLOBAL OPTIMIZATION, 2007, 37 (03) :449-465

[7] Continuity of solution maps of parametric quasiequilibrium problems [J].

Anh, Lam Quoc ;

Khanh, Phan Quoc .

JOURNAL OF GLOBAL OPTIMIZATION, 2010, 46 (02) :247-259

[8] Semicontinuity of the solution set of parametric multivalued vector quasiequilibrium problems [J].

Anh, LQ ;

Khanh, PQ .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 294 (02) :699-711

[9] Generalized vector quasi-equilibrium problems with applications [J].

Ansari, QH ;

Flores-Bazán, F .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 277 (01) :246-256

[10]

Bazan FF, 2001, SIAM J OPTIMIZ, V11, P675

← 1 2 3 4 →