Dual Variable Inertial Accelerated Algorithm for Split System of Null Point Equality Problems

Abstract

In this paper, we introduce a novel dual variable algorithm accelerated via inertial extrapolation for solving the generalized split inverse problem given as a task of finding the common null point equality of finite family of inverse-strongly monotone mappings in Hilbert spaces. The proposed method uses the dual variable and self-adaptive technique, along with an inertial strategy which aims at getting accelerated convergence. We establish the convergence Theorem of the proposed method under some suitable assumptions. We also apply our result to solve several types of problems. Our results improve and generalize the corresponding several known results announced by many others. Numerical experiments are presented to show the efficiency and comparative performance of the proposed algorithm.