Hybrid Extragradient Scheme for Split Variational Inclusion in Hilbert Spaces

jitsupa deepho

Abstract

In this paper, we propose a hybrid extragradient method to approximatea common solution set of split variational inclusion problem, a generalsystem of variational inequalities and fixed point set of a k-strictly pseudocontractivemapping in real Hilbert space. Our hybrid method is based on the well-knownextragradient method, viscosity approximation method, and Mann-type iterationmethod. Strong convergence theorem is established under some suitable conditionsin a real Hilbert space. Results presented in this paper may be viewed as a refinementand important generalizations of the previously known results announced bymany other authors.