A self-adaptive hybrid inertial algorithm for split feasibility problems in Banach spaces

Abstract

In this paper, we introduce a new self-adaptive hybrid algorithm of inertial form for solving Split Feasibility Problem (SFP) which also solve a Monotone Inclusion Problem (MIP) and a Fixed Point Problem (FPP) in $p$-uniformly convex and uniformly smooth Banach spaces. Motivated by the self-adaptive technique, we incorporate the inertial technique to accelerate the convergence of the proposed method. Under standard and mild assumption of monotonicity of the SFP associated mapping, we establish the strong convergence of the sequence generated by our algorithm which does not require a prior knowledge of the norm of the bounded linear operator. Some numerical examples are presented to illustrate the performance of our method as well as comparing it with some related methods in the literature.