Inertial algorithm with self-adaptive step size for split common null point and common fixed point problems for multivalued mappings in Banach spaces

Abstract

In this article we introduce an inertial iterative scheme with self-adaptive step size for finding a common solution of split common null point problem for a finite family of maximal monotone operators and fixed point problem for a finite family of multivalued demicontractive mappings between a Banach space and Hilbert space. Strong convergence result is obtained for the proposed algorithm. The self-adaptive step size ensures no requirement for a prior knowledge or estimate of the norm of the operator. The inertial term introduced in the algorithm is efficient, it helps to avoid imposing some strong conditions usually used for inertial-type algorithms by many authors. We give some applications of our results to game theory, split equilibrium and minimum-norm problems. Numerical experiment is also presented to demonstrate the efficiency of our proposed method as well as comparing with other existing method in the literature. Our results improve and generalize many well known results in this direction in the literature.