Yosida Approximation Iterative Methods for Split Monotone Variational Inclusion Problems

Abstract

In this paper, we present two iterative algorithms involving Yosida approximation operators for split monotone variational inclusion problems ( ${\text{S}}_{\text{p}}\text{MVIP}$ ). We prove the weak and strong convergence of the proposed iterative algorithms to the solution of ${\text{S}}_{\text{p}}\text{MVIP}$ in real Hilbert spaces. Our algorithms are based on Yosida approximation operators of monotone mappings such that the step size does not require the precalculation of the operator norm. To show the reliability and accuracy of the proposed algorithms, a numerical example is also constructed.