*Mathematical Methods in the Applied Sciences*Modified subgradient extragradient method for approximating of the
system of general equilibrium problem and fixed point problem

19 Feb 2020

22 Feb 2020

22 Feb 2020

20 Apr 2020

In this paper, we introduce the system of general equilibrium problem
(SGEP) and new subgradient extragradient by using the concept of the set
of solution of the modified variational inequality problem introduced by
\cite{kangtunyakarn}. Then, we establish and prove weak
and strong convergence theorem of the new subgradient extragradient
algorithm for finding the set of the solutions of the SGEP under some
suitable conditions of $\alpha_{n}$ and
$\beta_{n}$ with
$\alpha_{n}+\beta_{n}\leq
1$. Moreover, we apply our main theorem to prove weak and strong
convergence theorems for finding solutions of the generalized
equilibrium problem, the system of equilibrium problem, the variational
inequality problem and the general system of variational inequality
problem. In the last section, we give three numerical examples to
support our main result.