An inertial self-adaptive iterative algorithm for finding the common solutions to split feasibility and fixed point problems in specific Banach spaces

In this paper, we propose a new self adaptive iterative algorithm with an inertial technique for solving split feasibility problems and fixed point problems of relative nonexpansive mappings in p-uniformly convex and uniformly smooth Banach spaces. Under some appropriate assumptions imposed on the parameters and operators, we prove that the iterative sequence generated by our proposed algorithm converges strongly to a common solution of split feasibility problems and fixed point problems. Our algorithm does not require a prior knowledge of the norm of the bounded linear operator as we use a new self adaptive step size. Moreover, we give some numerical examples to show the effectiveness and feasibility of our algorithm.