An inertial extrapolation method for solving generalized split feasibility problems in real hilbert spaces

In this paper, we propose a new inertial extrapolation method for solving a certain class of generalized split feasibility problems in two real Hilbert spaces. We prove that the proposed method converges strongly to a minimum norm solution of the problem when the underlying operator is pseudomonotone and uniformly continuous which are much more weaker assumptions than the inverse strongly monotonicity assumptions used in the literature. Moreover, our method uses stepsizes that are generated at each iteration by some simple computations, which allows it to be easily implemented without the prior knowledge of the operator norm or the coefficient of a underlying operator. Furthermore, some examples and numerical experiments to show the efficiency and implementation of our method (in comparison with other methods in the literature) were also discussed in the framework of infinite dimensional Hilbert spaces.