Computational of generalized projection method for maximal monotone operators and a countable family of relatively quasi-nonexpansive mappings
Siwaporn Saewan, Poom Kumam · Optimization · 2013
We introduce a new hybrid projection method in mathematical programming for finding a common element of the set of common fixed points of a countable family of relatively quasi-nonexpansive mappings, the set of the variational inequality for an -inverse-strongly monotone operator, the set of solutions of the mixed equilibrium problem and a zero of a maximal monotone operator in the framework of a real Banach space. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. Furthermore, we give some numerical examples which support our main theorem in the last part.