scholarly journals Strong Convergence of Modified Inertial Mann Algorithms for Nonexpansive Mappings

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 462
Author(s):  
Bing Tan ◽  
Zheng Zhou ◽  
Songxiao Li

We investigated two new modified inertial Mann Halpern and inertial Mann viscosity algorithms for solving fixed point problems. Strong convergence theorems under some fewer restricted conditions are established in the framework of infinite dimensional Hilbert spaces. Finally, some numerical examples are provided to support our main results. The algorithms and results presented in this paper can generalize and extend corresponding results previously known in the literature.

2018 ◽  
Vol 12 (6) ◽  
pp. 255-270
Author(s):  
Jun Niu ◽  
Zheng Zhou ◽  
Jian-Qiang Zhang ◽  
Li-Juan Qin

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 167 ◽  
Author(s):  
Prasit Cholamjiak ◽  
Suparat Kesornprom ◽  
Nattawut Pholasa

In this work, we study the inclusion problem of the sum of two monotone operators and the fixed-point problem of nonexpansive mappings in Hilbert spaces. We prove the weak and strong convergence theorems under some weakened conditions. Some numerical experiments are also given to support our main theorem.


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