Algorithmic and analytical approach to the proximal split feasibility problem and fixed point problem
نویسندگان
چکیده
In this paper, we investigate the proximal split feasibility algorithm and fixed point problem in Hilbert spaces. We propose an iterative for finding a common element of solution L-Lipschitz pseudocontractive operator. demonstrate that considered converges strongly to investigated problems under some mild conditions.
منابع مشابه
Applications of Fixed-Point and Optimization Methods to the Multiple-Set Split Feasibility Problem
The multiple-set split feasibility problem requires finding a point closest to a family of closed convex sets in one space such that its image under a linear transformation will be closest to another family of closed convex sets in the image space. It can be amodel for many inverse problemswhere constraints are imposed on the solutions in the domain of a linear operator as well as in the operat...
متن کاملMultidirectional hybrid algorithm for the split common fixed point problem and application to the split common null point problem
In this article, a new multidirectional monotone hybrid iteration algorithm for finding a solution to the split common fixed point problem is presented for two countable families of quasi-nonexpansive mappings in Banach spaces. Strong convergence theorems are proved. The application of the result is to consider the split common null point problem of maximal monotone operators in Banach spaces. ...
متن کاملA fixed point approach to Nehari’s problem and its applications
We introduce a new approach to Nehari’s problem. This approach is based on some kind of fixed point theorem and allows us to obtain some useful generalizations of Nehari’s and Adamyan – Arov – Krein (AAK) theorems. Among those generalizations: descriptions of Hankel operators in weighted 2 spaces; descriptions of Hankel operators from Dirichlet type spaces to weighted Bergman spaces; commutant ...
متن کاملRegularized Methods for the Split Feasibility Problem
and Applied Analysis 3 However, 1.8 is, in general, ill posed. So regularization is needed. We consider Tikhonov’s regularization min x∈C fα : 1 2 ∥I − PQ ) Ax ∥∥2 1 2 α‖x‖, 1.9 where α > 0 is the regularization parameter. We can compute the gradient ∇fα of fα as ∇fα ∇f x αI A∗ ( I − PQ ) A αI. 1.10 Define a Picard iterates x n 1 PC ( I − γA∗I − PQ ) A αI )) x n 1.11 Xu 20 shown that if the SFP...
متن کاملStrong convergence theorem for solving split equality fixed point problem which does not involve the prior knowledge of operator norms
Our contribution in this paper is to propose an iterative algorithm which does not require prior knowledge of operator norm and prove a strong convergence theorem for approximating a solution of split equality fixed point problem for quasi-nonexpansive mappings in a real Hilbert space. So many have used algorithms involving the operator norm for solving split equality fixed point problem, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Filomat
سال: 2022
ISSN: ['2406-0933', '0354-5180']
DOI: https://doi.org/10.2298/fil2202439y