We introduce a new algorithm to approximate a solution of split variational inclusion problems of multivalued maximal monotone operators in uniformly convex and uniformly smooth Banach spaces under the Bregman distance. A strong convergence theorem for the above problem is established and several important known results are deduced as corollaries to it. As application, we solve a split minimization problem and provide a numerical example to support better findings of our result.
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Keywords: Split variational inclusion problem, maximal monotone operators, Bregman distance, strong convergence, uniformly convex and uniformly smooth Banach space
@article{RO_2021__55_S1_S2417_0,
author = {Abbas, Mujahid and G\"ursoy, Faik and Ibrahim, Yusuf and Khan, Abdul Rahim},
title = {Split variational inclusions for {Bregman} multivalued maximal monotone operators},
journal = {RAIRO. Operations Research},
pages = {S2417--S2431},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
doi = {10.1051/ro/2020085},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2020085/}
}
TY - JOUR AU - Abbas, Mujahid AU - Gürsoy, Faik AU - Ibrahim, Yusuf AU - Khan, Abdul Rahim TI - Split variational inclusions for Bregman multivalued maximal monotone operators JO - RAIRO. Operations Research PY - 2021 SP - S2417 EP - S2431 VL - 55 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2020085/ DO - 10.1051/ro/2020085 LA - en ID - RO_2021__55_S1_S2417_0 ER -
%0 Journal Article %A Abbas, Mujahid %A Gürsoy, Faik %A Ibrahim, Yusuf %A Khan, Abdul Rahim %T Split variational inclusions for Bregman multivalued maximal monotone operators %J RAIRO. Operations Research %D 2021 %P S2417-S2431 %V 55 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2020085/ %R 10.1051/ro/2020085 %G en %F RO_2021__55_S1_S2417_0
Abbas, Mujahid; Gürsoy, Faik; Ibrahim, Yusuf; Khan, Abdul Rahim. Split variational inclusions for Bregman multivalued maximal monotone operators. RAIRO. Operations Research, Tome 55 (2021), pp. S2417-S2431. doi: 10.1051/ro/2020085
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