Abstract
In this paper, we introduce a new iterative method using an inertial technique for approximating a common fixed point of an infinite family of nonexpansive mappings in a Hilbert space. The proposed method’s weak convergence theorem was established under some suitable conditions. Furthermore, we applied our main results to solve convex minimization problems and image restoration problems.
Highlights
Let us first mention a mathematical scheme for an image restoration problem, as well as some algorithms that will be employed to solve it
In order to find the solution of the problem (1), we minimize the additive noise to approximate the original image by using the method known as the least squares (LS)
Motivated and inspired by all the works mentioned above, in this article, we introduced a new iterative method for the approximation of a common fixed point of an infinite family of nonexpansive mappings in Hilbert spaces
Summary
Let us first mention a mathematical scheme for an image restoration problem, as well as some algorithms that will be employed to solve it. To improve the original LS (2) and classical regularization such as subset selection and ridge regression (3) for solving (1), Tibshirani [5] defined a new method, called the least absolute shrinkage and selection operator (LASSO) model, as the following form:. This notion was suggested by Beck and Teboulle [6] They proved the FISTA’s convergence rate and applied it to solve image restoration problems. Motivated and inspired by all the works mentioned above, in this article, we introduced a new iterative method for the approximation of a common fixed point of an infinite family of nonexpansive mappings in Hilbert spaces. We present the brief conclusion of our work
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