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

[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.

[发布日期] 2020-09-01

[关键词] Iterative method;Strong convergence;Fixed point problem;Split monotone variational inclusion problem;Nonexpansive mapping;Variational inequality problem;47J25;49J40;47H09;90C99