NEW TECHNIQUES TO FIND THE SWIFT CONVERGENCE USING INERTIAL EXTRAPOLATION SCHEME IN THE CAYLEY VARIATIONAL INCLUSION PROBLEM

Abstract In this study, we utilize an inertial extrapolation scheme to achieve rapid convergence for the Cayley variational inclusion problem and the equivalent Cayley resolvent equation problem. We have outlined several strategies to address both problems. Still, our primary focus is on validating the rapid convergence for the Cayley variational inclusion problem in a real Banach space and the Cayley resolvent equation problem in a q-uniformly smooth Banach space. We employ an inertial extrapolation strategy in both cases to achieve rapid convergence. A mathematical experiment is presented to demonstrate Swift Convergence.