TY - JOUR
T1 - Convergence results of forward–backward method for a zero of the sum of maximally monotone mappings in Banach spaces
AU - Wega, Getahun Bekele
AU - Zegeye, Habtu
N1 - Publisher Copyright:
© 2020, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.
PY - 2020/9/1
Y1 - 2020/9/1
N2 - The purpose of this paper is to study a forward–backward algorithm for approximating a zero of the sum of maximally monotone mappings in the setting of Banach spaces. Under some mild conditions, we prove a new strong convergence theorem for the algorithm produced by the method in real reflexive Banach spaces. In addition, we give some applications to the minimization problems. Finally, we provide a numerical example, which supports our main result. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.
AB - The purpose of this paper is to study a forward–backward algorithm for approximating a zero of the sum of maximally monotone mappings in the setting of Banach spaces. Under some mild conditions, we prove a new strong convergence theorem for the algorithm produced by the method in real reflexive Banach spaces. In addition, we give some applications to the minimization problems. Finally, we provide a numerical example, which supports our main result. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.
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U2 - 10.1007/s40314-020-01246-z
DO - 10.1007/s40314-020-01246-z
M3 - Article
AN - SCOPUS:85088095358
SN - 2238-3603
VL - 39
JO - Computational and Applied Mathematics
JF - Computational and Applied Mathematics
IS - 3
M1 - 223
ER -