Two inertial projection-type methods for solving pseudo-monotone variational inequalities with application to image deblurring problem

Abstract

Our purpose is to propose two different type of inertial algorithms for approximating a solution of pseudo-monotone variational inequality problem in the framework of Banach spaces. The proposed algorithms are established by using Mann’s iterative method and single projection type method with adaptive step-size. Strong convergence theorems for minimum-norm solution of the variational inequality problem are established without the prior knowledge of the Lipschitz constant of the mapping. Finally, some numerical experiments are performed to illustrate the advantage of the proposed methods and numerical experiments in image recovery are also presented. Our results generalize and improve some known results existing in the current literature.</p