Two Novel Cyclic Projection Algorithms for Solving Split Mixed Variational Inequalities Beyond Co‐Coerciveness

ABSTRACT We investigate the split mixed variational inequality problem with multiple output sets in real Hilbert spaces. By incorporating multiple inertial steps, utilizing a general index control mapping, and employing either hybrid methods or shrinking projection techniques, we introduce two novel cyclic projection algorithms for solving this problem without requiring the inverse strong monotonicity assumption on the associated operators. In addition, the control parameters are designed to be self‐adaptive.