Strong convergence of a general viscosity explicit rule for the sum of two monotone operators in hilbert spaces

Abstract

© 2019, Wilmington Scientific Publisher. All rights reserved. In this paper, we study a general viscosity explicit rule for approximating the solutions of the variational inclusion problem for the sum of two monotone operators. We then prove its strong convergence under some new conditions on the parameters in the framework of Hilbert spaces. As applications, we apply our main result to the split feasibility problem and the LASSO problem. We also give some numerical examples to support our main result. The results presented in this paper extend and improve the corresponding results in the literature.