carpathian_2024_40_2_275_291_001

Modified General Inertial Mann and General Inertial Viscosity Algorithms for Fixed Point and Common Fixed Point Problems with Applications


Gebregiorgis, Solomon, Kumam, Poom and Seangwattana, Thidaporn


Full PDF

carpathian_2024_40_2_275_291

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.

 

 

Additional Information

Author(s)

 Kumam, Poom,  Gebregiorgis, Solomon, Seangwattana, Thidaporn

DOI

https://doi.org/10.37193/CJM.2024.02.04