A system of nonlinear set-valued implicit variational inclusions in real Banach spaces
Commun. Korean Math. Soc. 2010 Vol. 25, No. 1, 129-137
https://doi.org/10.4134/CKMS.2010.25.1.129
Printed March 1, 2010
Chuanzhi Bai and Qing Yang
Huaiyin Normal University, Huaiyin Normal University
Abstract : 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
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