VISCOSITY EXTRAGRADIENT METHOD WITH ARMIJO LINESEARCH RULE FOR PSEUDOMONOTONE EQUILIBRIUM PROBLEM AND FIXED POINT PROBLEM IN HILBERT SPACES

被引：2

作者：

Li, Gaobo ^{[1
]}

Lu, Yanxia ^{[2
]}

Cho, Yeol Je ^{[3
,4
]}

机构：

[1] Shan Dong Womens Univ, Sch Educ, Jinan 056210, Peoples R China

[2] North China Elect Power Univ, Dept Math & Phys, Baoding 071003, Peoples R China

[3] Gyeongsang Natl Univ, Dept Math Educ, Jinju 52828, South Korea

[4] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Sichuan, Peoples R China

来源：

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2019年 / 50卷 / 04期

关键词：

Nonexpansive mappings; equilibrium problems; Hilbert spaces; ALGORITHMS;

D O I：

10.1007/s13226-019-0363-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we introduce a viscosity extragradient method with Armijo linesearch rule to find a common element of solution set of a pseudomonotone equilibrium problem and fixed point set of a nonexpansive nonself-mapping in Hilbert space. The strong convergence of the algorithm is proved. As the application, a common fixed point theorem for two nonexpansive nonself-mappings is proved. Finally, some numerical examples are given to illustrate the effectiveness of the algorithm. Our result improves the ones of others in the literature.

引用

下载

页码：903 / 921

页数：19

共 50 条

[21] The Ishikawa Subgradient Extragradient Method for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces
Duc, Manh Hy
Thanh, Ha Nguyen Thi
Huyen, Thanh Tran Thi
Dinh, Bui Van
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2020, 41 (09) : 1065 - 1088
[22] Viscosity extragradient with modified inertial method for solving equilibrium problems and fixed point problem in Hadamard manifold
Ndlovu, P. V.
Jolaoso, L. O.
Aphane, M.
Abass, H. A.
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2024, 2024 (01)
[23] Viscosity extragradient with modified inertial method for solving equilibrium problems and fixed point problem in Hadamard manifold
P. V. Ndlovu
L. O. Jolaoso
M. Aphane
H. A. Abass
Journal of Inequalities and Applications, 2024
[24] The extragradient-Armijo method for pseudomonotone equilibrium problems and strict pseudocontractions
Pham Ngoc Anh
Nguyen Duc Hien
FIXED POINT THEORY AND APPLICATIONS, 2012,
[25] The extragradient-Armijo method for pseudomonotone equilibrium problems and strict pseudocontractions
Pham Ngoc Anh
Nguyen Duc Hien
Fixed Point Theory and Applications, 2012
[26] A self-adaptive extragradient method for fixed-point and pseudomonotone equilibrium problems in Hadamard spaces
Aremu, Kazeem Olalekan
Jolaoso, Lateef Olakunle
Oyewole, Olawale Kazeem
FIXED POINT THEORY AND ALGORITHMS FOR SCIENCES AND ENGINEERING, 2023, 2023 (01):
[27] A modified self-adaptive extragradient method for pseudomonotone equilibrium problem in a real Hilbert space with applications
Rehman, Habib ur
Kumam, Poom
Dong, Qiao-Li
Cho, Yeol Je
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (05) : 3527 - 3547
[28] A New Iterative Method for Finding Common Solutions of Generalized Equilibrium Problem and Fixed Point Problem in Hilbert Spaces
Min LIUShi Sheng ZHANG Department of MathematicsYibin UniversitySichuan PRChina
数学研究与评论, 2010, 30 (06) : 1061 - 1070
[29] A New Iterative Method for Finding Common Solutions of Generalized Equilibrium Problem and Fixed Point Problem in Hilbert Spaces
Min LIU
Journal of Mathematical Research with Applications, 2010, (06) : 1061 - 1070
[30] A BREGMAN HYBRID EXTRAGRADIENT METHOD FOR SOLVING PSEUDOMONOTONE EQUILIBRIUM AND FIXED POINT PROBLEMS
Jantakarn K.
Kaewcharoen A.
Journal of Nonlinear Functional Analysis, 2022, 2022

← 1 2 3 4 5 →