TY - JOUR
T1 - Approximating solutions of the sum of a finite family of maximally monotone mappings in Hilbert spaces
AU - Wega, Getahun Bekele
AU - Zegeye, Habtu
AU - Boikanyo, Oganeditse A.
N1 - Publisher Copyright:
© 2019, Tusi Mathematical Research Group (TMRG).
PY - 2020/5/1
Y1 - 2020/5/1
N2 - The purpose of this paper is to study the method of approximation for a zero of the sum of a finite family of maximally monotone mappings using viscosity type Douglas–Rachford splitting algorithm and prove some strong convergence theorems of the proposed algorithm under suitable conditions. In addition, we give some applications to the minimization problems. Finally, a numerical example which supports our main result is presented. 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 the method of approximation for a zero of the sum of a finite family of maximally monotone mappings using viscosity type Douglas–Rachford splitting algorithm and prove some strong convergence theorems of the proposed algorithm under suitable conditions. In addition, we give some applications to the minimization problems. Finally, a numerical example which supports our main result is presented. 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/s43036-019-00026-9
DO - 10.1007/s43036-019-00026-9
M3 - Article
AN - SCOPUS:85079594002
SN - 2538-225X
VL - 5
SP - 359
EP - 370
JO - Advances in Operator Theory
JF - Advances in Operator Theory
IS - 2
ER -