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- Title
Modified General Inertial Mann and General Inertial Viscosity Algorithms for Fixed Point and Common Fixed Point Problems with Applications.
- Authors
GEBREGIORGIS, SOLOMON; KUMAM, POOM; SEANGWATTANA, THIDAPORN
- Abstract
In this paper, we propose a modified general inertial Mann algorithm and prove that it generates a sequence which converges weakly to a fixed point of a nonexpansive mapping in Hilbert spaces. Moreover, by using the viscosity method, we introduce a general inertial viscosity algorithm and prove that it generates a sequence which converges strongly to a common fixed point of a countable family of nonexpansive operators. We also derive schemes for solving constrained convex optimization, monotone inclusion, and nonsmooth convex optimization problems. Finally, we apply one of our proposed algorithms to solve image restoration problem.
- Subjects
VISCOSITY; IMAGE reconstruction; NONSMOOTH optimization; NONEXPANSIVE mappings; CONSTRAINED optimization; HILBERT space; FIXED point theory
- Publication
Carpathian Journal of Mathematics, 2024, Vol 40, Issue 2, p275
- ISSN
1584-2851
- Publication type
Article
- DOI
10.37193/CJM.2024.02.04