A unified framework for three accelerated extragradient methods and further acceleration for variational inequality problems

The main strategy of this paper is intended to speed up the convergence inertial Mann iterative method and further it through normal S-iterative for a certain class nonexpansive-type operators that are linked with variational inequality problems. Our new theory permits us settle down difficulty unification Korpelevich’s extragradient method, Tseng’s extragardient subgardient solving problems an auxiliary algorithmic operator, which associated seed operator. establishes interesting fact relaxed methods do influence much more on behaviour. Finally, numerical experiments carried out illustrate methods; in particular, may have number advantages over other computing solutions many cases.