Accelerated modified inertial Mann and viscosity algorithms to find a fixed point of α−inverse strongly monotone operators

Abstract

In this paper, strong convergence results for α−inverse strongly monotone operators under new algorithms in the framework of Hilbert spaces are discussed. Our algorithms are the combination of the inertial Mann forward-backward method with the CQ-shrinking projection method and viscosity algorithm. Our methods lead to an acceleration of modified inertial Mann Halpern and viscosity algorithms. Later on, numerical examples to illustrate the applications, performance, and effectiveness of our algorithms are presented.

Keywords

• inertial mann forward-backward method
• strong convergence theorems
• viscosity algorithm
• cq-projection method
• shrinking projection method