Split variational inclusions for Bregman multivalued maximal monotone operators

¹ Department of Mathematics, Government College University, Katchery Road, Lahore 54000, Pakistan
² Department of Mathematics, Adiyaman University, Adiyaman 02040, Turkey
³ Department of Mathematics, Sa’adatu Rimi College of Education, Kumbotso Kano, P.M.B. 3218 Kano, Nigeria
⁴ Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

^* Corresponding author: faikgursoy02@hotmail.com

Received: 27 January 2020
Accepted: 29 July 2020

Abstract

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.