Modified inertial subgradient extragradient method in reflexive Banach spaces

被引:0
作者
Bashir Ali
G. C. Ugwunnadi
M. S. Lawan
A. R. Khan
机构
[1] Bayero University,Department of Mathematical Sciences
[2] University of Eswatini,Department of Mathematics
[3] Kaduna Polytechnic,Department of Mathematics and Statistics
[4] King Fahd University of Petroleum and Minerals,Department of Mathematics and Statistics
[5] Sefako Makgatho Health Sciences University,Department of Mathematics and Applied Mathematics
来源
Boletín de la Sociedad Matemática Mexicana | 2021年 / 27卷
关键词
Bregman distance; Bregman Demigeneralized map; Monotone map; Subgradient extragradient method; Fixed point; 47H09; 47J25;
D O I
暂无
中图分类号
学科分类号
摘要
In this paper, we study a modified inertial subgradient extragradient algorithm in reflexive Banach spaces and prove a strong convergence theorem for approximating common solutions of a fixed point equation of a demigeneralized mapping and a variational inequality problem of a monotone and Lipschitz mapping. Our result extends and improves important recent results announced by many authors.
引用
收藏
相关论文
共 64 条
[1]  
Ali B(2019)Inertial algorithm for solving fixed point and generalized mixed equilibrium problems in Banach spaces Pan Am. Math. J. 29 64-83
[2]  
Ezeora JN(2013)Convergence of a hybrid iterative scheme for fixed point of nonexpansive maps, solution of equilibrium problem and variational inequality problem J. Math. 29 115-136
[3]  
Lawan MS(2018)A new convergence theorem for families of asymptotically nonexpansive maps and solution of variational inequality problems Afr. Math. 60 321-337
[4]  
Ali B(2014)A new approximation method for common fixed point of families of nonexpansive maps and solution of variational inequality problem Annali Dell’universita’ Diferrara 228 443-467
[5]  
Ali B(1969)Gradient of convex function Trans. Am. Math. Soc. 4 27-67
[6]  
Ugwunnadi GC(1997)Legendre function and the method of Bregman projections J. Convex Anal. 3 615-647
[7]  
Ali B(2001)Essential smoothness, essential strict convexity, and Legendre functions in Banach Spaces Commun. Contemp. Math. 7 200-217
[8]  
Mohammed M(1967)The realization method for finding the common point of convex set and its application to solution of convex programming USSR Comput. Math. Phys. 1–39 2006-9507
[9]  
Ugwunnadi GC(2006)Bregman distances, totally convex functions and a method of solving operator equations in Banach spaces Abstr. Appl. Anal. 217 9499-218
[10]  
Asplund E(2011)Convergence of hybrid steepest decent method for variational inequalities in Banach spaces Appl. Math. Compt. 2 203-353