TY - JOUR
T1 - A Method of approximation for a zero of the sum of maximally monotone mappings in Hilbert spaces
AU - Wega, Getahun Bekele
AU - Zegeye, Habtu
N1 - Funding Information:
The authors thank the anonymous referees for useful suggestions which improved the contents of this paper. Funding: The first author gratefully acknowledges the funding received from Simons Foundation based at Botswana International University of Science and Technology (BIUST), Palapye, Botswana.Declaration of Competing Interest: None.The publisher wishes to inform readers that the article “A Method of approximation for a zero of the sum of maximally monotone mappings in Hilbert spaces” was originally published by the previous publisher of the Arab Journal of Mathematical Sciences and the pagination of this article has been subsequently changed. There has been no change to the content of the article. This change was necessary for the journal to transition from the previous publisher to the new one. The publisher sincerely apologises for any inconvenience caused. To access and cite this article, please use Wega, G. B., Zegeye, H. (2019), “A Method of approximation for a zero of the sum of maximally monotone mappings in Hilbert spaces”, Arab Journal of Mathematical Sciences, Vol. 27 No. 1, pp. 26-40. The original publication date for this paper was 22/05/2019.
Funding Information:
The authors thank the anonymous referees for useful suggestions which improved the contents of this paper. Funding : The first author gratefully acknowledges the funding received from Simons Foundation based at Botswana International University of Science and Technology (BIUST), Palapye, Botswana.Declaration of Competing Interest : None.The publisher wishes to inform readers that the article ?A Method of approximation for a zero of the sum of maximally monotone mappings in Hilbert spaces? was originally published by the previous publisher of the Arab Journal of Mathematical Sciences and the pagination of this article has been subsequently changed. There has been no change to the content of the article. This change was necessary for the journal to transition from the previous publisher to the new one. The publisher sincerely apologises for any inconvenience caused. To access and cite this article, please use?Wega, G. B., Zegeye, H. (2019), ?A Method of approximation for a zero of the sum of maximally monotone mappings in Hilbert spaces?, Arab Journal of Mathematical Sciences, Vol. 27 No. 1, pp. 26-40. The original publication date for this paper was 22/05/2019.
Publisher Copyright:
© 2019, Getahun Bekele Wega and Habtu Zegeye.
PY - 2021/4/20
Y1 - 2021/4/20
N2 - Our purpose of this study is to construct an algorithm for finding a zero of the sum of two maximally monotone mappings in Hilbert spaces and discus its convergence. The assumption that one of the mappings is (Formula presented.) -inverse strongly monotone is dispensed with. In addition, we give some applications to the minimization problem. Our method of proof is of independent interest. 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 - Our purpose of this study is to construct an algorithm for finding a zero of the sum of two maximally monotone mappings in Hilbert spaces and discus its convergence. The assumption that one of the mappings is (Formula presented.) -inverse strongly monotone is dispensed with. In addition, we give some applications to the minimization problem. Our method of proof is of independent interest. 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.
UR - http://www.scopus.com/inward/record.url?scp=85086319363&partnerID=8YFLogxK
U2 - 10.1016/j.ajmsc.2019.05.004
DO - 10.1016/j.ajmsc.2019.05.004
M3 - Article
AN - SCOPUS:85086319363
VL - 27
SP - 26
EP - 40
JO - Arab Journal of Mathematical Sciences
JF - Arab Journal of Mathematical Sciences
SN - 1319-5166
IS - 1
ER -