An Inertial Type Subgradient Extragradient Method for Common Fixed Point and Variational Inequalities Problems in Real

In this paper, we introduce a new inertial type algorithm with self - adaptive step - size technique for approximating a common element of the set of solutions of pseudomonotone variational inequality problem and the set of common fixed point of a finite family of generic generalized nonspreading mappings in uniformly smooth and 2 - uniformly convex real Banach space. Furthermore, we prove a strong convergence theorem of our algorithm without prior knowledge of the Lipschitz constant of the operator under some mild assumptions. We also give numerical examples to illustrate the performance of our algorithm. Our result generalize and improve many existing results in the literature.