A new accelerated algorithm for solving variational inequalities over the solution of multiple set split common fixed point problem

In this paper, we study a variational inequality problem which is defined over the the solution of multiple set split common fixed point problem for a finite family of generalized demimetric mappings. We present an accelerated steepest descent algorithm for solving this problem and then establish strong convergence of the proposed method under standard and mild conditions. We apply our proposed algorithm to solve some problems, including variational inequalities over multiple set split feasibility problem, variational inequalities over multiple set split zero point problem and the convex optimization problem.