A THREE-TERM INERTIAL DERIVATIVE-FREE PROJECTION METHOD FOR CONVEX CONSTRAINED MONOTONE EQUATIONS

Let $\mathfrak{R}^n$ be an Euclidean space and $ g: \mathfrak{R}^n \rightarrow \mathfrak{R}^n$ be a monotone and continuous mapping. Suppose the convex constrained nonlinear monotone equation problem $x \in \mathfrak{C} ~\text{s.t} ~ g(x) = 0$ has a solution. In this paper, we construct an inertial-type algorithm based on the three-term derivative-free projection method (TTMDY) for convex constrained monotone nonlinear equations. Under some standard assumptions, we establish its global convergence to a solution of the convex constrained nonlinear monotone equation. Furthermore, the proposed algorithm converges much faster than the existing non-inertial algorithm (TTMDY) for convex constrained monotone equations.