Approximation method for monotone inclusion problems in real Banach spaces with applications

Journal of Inequalities and Applications

Poom Kumam¹  Duangkamon Kitkuan²  Anantachai Padcharoen²  Thidaporn Seangwattana³  Abubakar Adamu⁴ 

[1] Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT);Department of Mathematics, Faculty of Science and Technology, Rambhai Barni Rajabhat University;Faculty of Science Energy and Environment, King Mongkut’s University of Technology North Bangkok;Mathematics Institute, African University of Science and Technology;

关键词: Monotone;    Convex minimization;    Zeros;    Image restoration;    Signal recovery;   

DOI  :  10.1186/s13660-022-02805-0

来源: DOAJ

【 摘 要 】

Abstract In this paper, we introduce an inertial Halpern-type iterative algorithm for approximating a zero of the sum of two monotone operators in the setting of real Banach spaces that are 2-uniformly convex and uniformly smooth. Strong convergence of the sequence generated by our proposed algorithm is established by means of some new geometric inequalities proved in this paper that are of independent interest. Furthermore, numerical simulations in image restoration and compressed sensing problems are also presented. Finally, the performance of the proposed method is compared with that of some existing methods in the literature.

【 授权许可】

Unknown