Adaptive inertial Yosida approximation iterative algorithms for split variational inclusion and fixed point problems

Abstract

In this paper, we present self-adaptive inertial iterative algorithms involving Yosida approximation to investigate a split variational inclusion problem (SVIP) and common solutions of a fixed point problem (FPP) and SVIP in Hilbert spaces. We analyze the weak convergence of the proposed iterative algorithm to explore the approximate solution of the SVIP and strong convergence to estimate the common solution of the SVIP and FPP under some mild suppositions. A numerical example is demonstrated to validate the theoretical findings, and comparison of our iterative methods with some known schemes is outlined.

Keywords

• split variational inclusion
• fixed point problem
• yosida approximation
• algorithms
• weak convergence
• strong convergence