Three new iterative methods for solving inclusion problems and related problems

In this paper, we study the variational inclusion problem which consists of finding zeros of the sum of a single and multivalued mappings in real Hilbert spaces. Motivated by the viscosity approximation, projection and contraction and inertial forward–backward splitting methods, we introduce two new...

Full description

Saved in:
Bibliographic Details
Published inComputational & applied mathematics Vol. 39; no. 3
Main Authors Gibali, Aviv, Thong, Duong Viet, Vinh, Nguyen The
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.09.2020
Springer Nature B.V
Subjects
Applications of Mathematics
Applied physics
Approximation
Computational mathematics
Computational Mathematics and Numerical Analysis
Hilbert space
Iterative methods
Mathematical analysis
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Splitting
65K15
Viscosity method
68W10
47H09
Zero point
47J25
65Y05
Inertial forward–backward splitting method
Projection and contraction method
Online AccessGet full text

Cover

More Information
Summary:In this paper, we study the variational inclusion problem which consists of finding zeros of the sum of a single and multivalued mappings in real Hilbert spaces. Motivated by the viscosity approximation, projection and contraction and inertial forward–backward splitting methods, we introduce two new forward–backward splitting methods for solving this variational inclusion. We present weak and strong convergence theorems for the proposed methods under suitable conditions. Our work generalize and extend some related results in the literature. Several numerical examples illustrate the potential applicability of the methods and comparisons with related methods emphasize it further.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-020-01215-6