An iterative scheme for split monotone variational inclusion, variational inequality and fixed point problems

Advances in Difference Equations

article

Alansari, Monairah¹  Farid, Mohammad²  Ali, Rehan³ 

[1] King Abdulaziz University;Deanship of Educational Services, Qassim University;Department of Mathematics

关键词: Iterative method;    Strong convergence;    Fixed point problem;    Split monotone variational inclusion problem;    Nonexpansive mapping;    Variational inequality problem;   

DOI  :  10.1186/s13662-020-02942-0

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

We propose and analyze a new type iterative algorithm to find a common solution of split monotone variational inclusion, variational inequality, and fixed point problems for an infinite family of nonexpansive mappings in the framework of Hilbert spaces. Further, we show that a sequence generated by the algorithm converges strongly to common solution. Furthermore, we list some consequences of our established theorem. Finally, we provide a numerical example to demonstrate the applicability of the algorithm. We emphasize that the result accounted in manuscript unifies and extends various results in this field of study.

【 授权许可】

CC BY