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In this paper, we suggest and analyze a new system of extended regularized nonconvex variational inequalities and prove the equivalence between the aforesaid system and a fixed point problem. We introduce a new perturbed projection iterative algorithm with mixed errors to find the solution of the system of extended regularized nonconvex variational inequalities. Furthermore, under moderate assumptions, we research the convergence analysis of the suggested iterative algorithm. [ABSTRACT FROM AUTHOR]

The split equality problem is a generalization of the split feasibility problem, meanwhile it is a special case of multiple-sets split equality problems. In this paper, we propose an iterative algorithm for solving the multiple-sets split equality problem whose iterative step size is split self-adaptive. The advantage of the split self-adaptive step size is that it could be obtained directly from the iterative procedure without needing to have any information of the spectral norm of the related operators. Under suitable conditions, we establish the theoretical convergence of the algorithm proposed in Hilbert spaces, and several numerical results confirm the effectiveness of the algorithm proposed. [ABSTRACT FROM AUTHOR]