Communications of the
Korean Mathematical Society CKMS

In this paper, we introduce and study a system of nonlinear set-valued implicit variational inclusions (SNSIVI) with relaxed cocoercive mappings in real Banach spaces. By using resolvent operator technique for $M$-accretive mapping, we construct a new class of iterative algorithms for solving this class of system of set-valued implicit variational inclusions. The convergence of iterative algorithms is proved in $q$-uniformly smooth Banach spaces. Our results generalize and improve the corresponding results of recent works.

Keywords: system of nonlinear set-valued implicit variational inclusion, resolvent operator, $M$-accretive mapping, iterative algorithm, convergence

MSC numbers: Primary 49J40, 47H04