An Iterative Method for Split Variational Inclusion Problem and Split Fixed Point Problem for Averaged Mappings  

作　　者：Kaiwen Wang Yali Zhao Ziru Zhao Kaiwen Wang;Yali Zhao;Ziru Zhao(School of Mathematical Science, Bohai University, Jinzhou, China)

机构地区：[1]School of Mathematical Science, Bohai University, Jinzhou, China

出　　处：《Journal of Applied Mathematics and Physics》2023年第6期1541-1556,共16页应用数学与应用物理（英文）

摘　　要：In this paper, we use resolvent operator technology to construct a viscosity approximate algorithm to approximate a common solution of split variational inclusion problem and split fixed point problem for an averaged mapping in real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and split fixed point problem for averaged mappings which is also the unique solution of the variational inequality problem. The results presented here improve and extend the corresponding results in this area.In this paper, we use resolvent operator technology to construct a viscosity approximate algorithm to approximate a common solution of split variational inclusion problem and split fixed point problem for an averaged mapping in real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and split fixed point problem for averaged mappings which is also the unique solution of the variational inequality problem. The results presented here improve and extend the corresponding results in this area.

关 键 词：Split Variational Inclusion Problem Split Fixed Point Problem Iterative Algorithm Averaged Mapping CONVERGENCE 

分 类 号：O17[理学—数学]