A NEW MAPPING FOR FINDING A COMMON SOLUTION OF SPLIT GENERALIZED EQUILIBRIUM PROBLEM, VARIATIONAL INEQUALITY PROBLEM AND FIXED POINT PROBLEM

被引：6

作者：

Farid, Mohammad ^{[1
]}

Kazmi, Kaleem Raza ^{[2
,3
]}

机构：

[1] Qassim Univ, Unaizah Coll Engn, Buraydah 51911, Saudi Arabia

[2] King Abdulaziz Univ, Dept Math, Fac Sci & Arts Rabigh, Jeddah, Saudi Arabia

[3] Aligarh Muslim Univ, Dept Math, Aligarh 202002, Uttar Pradesh, India

来源：

KOREAN JOURNAL OF MATHEMATICS | 2019年 / 27卷 / 02期

关键词：

Split generalized equilibrium problem; Variational inequality problem; Fixed-point problem; Nonexpansive mappings; VISCOSITY APPROXIMATION METHODS; ITERATIVE METHOD; CONVERGENCE;

D O I：

10.11568/kjm.2019.27.2.297

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we introduce and study a general iterative algorithm to approximate a common solution of split generalized equilibrium problem, variational inequality problem and fixed point problem for a finite family of nonexpansive mappings in real Hilbert spaces. Further, we prove a strong convergence theorem for the sequences generated by the proposed iterative scheme. Finally, we derive some consequences from our main result. The results presented in this paper extended and unify many of the previously known results in this area.

引用

页码：297 / 327

页数：31

共 22 条

[1]

Bauschke HH, 2011, CMS BOOKS MATH, P1, DOI 10.1007/978-1-4419-9467-7

[2]

Blum E., 1994, Mathematics Student, V63, P123

[3]

Byrne C, 2012, J NONLINEAR CONVEX A, V13, P759

[4] A hybrid iterative scheme for mixed equilibrium problems and fixed point problems [J].

Ceng, Lu-Chuan ;

Yao, Jen-Chih .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 214 (01) :186-201

[5] Algorithms for the Split Variational Inequality Problem [J].

Censor, Yair ;

Gibali, Aviv ;

Reich, Simeon .

NUMERICAL ALGORITHMS, 2012, 59 (02) :301-323

[6] A unified approach for inversion problems in intensity-modulated radiation therapy [J].

Censor, Yair ;

Bortfeld, Thomas ;

Martin, Benjamin ;

Trofimov, Alexei .

PHYSICS IN MEDICINE AND BIOLOGY, 2006, 51 (10) :2353-2365

[7]

Combettes PL, 2005, J NONLINEAR CONVEX A, V6, P117

[8] COMMON SOLUTIONS TO SOME SYSTEMS OF VARIATIONAL INEQUALITIES AND FIXED POINT PROBLEMS [J].

Djafari-Rouhani, B. ;

Kazmi, K. R. ;

Farid, Mohd. .

FIXED POINT THEORY, 2017, 18 (01) :167-190

[9] ON SOME NON-LINEAR ELLIPTIC DIFFERENTIAL-FUNCTIONAL EQUATIONS [J].

HARTMAN, P ;

STAMPACCHIA, G .

ACTA MATHEMATICA UPPSALA, 1966, 115 (3-4) :271-+

[10] A new mapping for finding common solutions of equilibrium problems and fixed point problems of finite family of nonexpansive mappings [J].

Kangtunyakarn, Atid ;

Suantai, Suthep .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (10) :4448-4460

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