Halpern-Type Inertial Iteration Methods with Self-Adaptive Step Size for Split Common Null Point Problem

Abstract

In this paper, two Halpern-type inertial iteration methods with self-adaptive step size are proposed for estimating the solution of split common null point problems (SpCNPP) in such a way that the Halpern iteration and inertial extrapolation are computed simultaneously in the beginning of each iteration. We prove the strong convergence of sequences driven by the suggested methods without estimating the norm of bounded linear operator when certain appropriate assumptions are made. We demonstrate the efficiency of our iterative methods and compare them with some related and well-known results using relevant numerical examples.

Keywords

• split common null point problem
• Halpern
• inertial
• self adaptive algorithms
• strong convergence