RELAXED DOUBLE INERTIAL TSENG'S EXTRAGRADIENT METHOD FOR SOLVING NON-LIPSCHITZ SPLIT MONOTONE VARIATIONAL INCLUSION PROBLEMS WITH FIXED POINT CONSTRAINTS

In the recent years, the split monotone variational inclusion problem has received great research attention due to its wide areas of application. However, a review of the literature shows that the existing results in this direction are not applicable when the associated single-valued operators are non Lipschitz. In this article, we propose a new relaxed double inertial Tseng's extragradient method with self-adaptive step sizes for solving split monotone variational inclusion problem (SMVIP) involving non-Lipschitz operators and a fixed point problem of strict pseudocontractive mappings. Under more relaxed assumptions, we prove that our proposed scheme converges strongly to a minimum-norm solution of the aforementioned problem in real Hilbert spaces. We point out that while the operators are non-Lipschitz, our method does not involve linesearch procedure which is known to be time-consuming, but we employ a more efficient self-adaptive step size technique that generates non monotonic sequence of step sizes at each iteration. Results of the numerical experiments demonstrate the comparative advantage of our method over existing methods in the literature. Our result extends and complements several existing results in the direction of this research in a unified way.