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Open AccessArticle

Strong Convergence of Modified Inertial Mann Algorithms for Nonexpansive Mappings

Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
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Mathematics 2020, 8(4), 462; https://doi.org/10.3390/math8040462 (registering DOI)
Received: 25 February 2020 / Revised: 9 March 2020 / Accepted: 21 March 2020 / Published: 25 March 2020
(This article belongs to the Special Issue Nonlinear Analysis and Optimization)
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.
Keywords: Halpern algorithm; viscosity algorithm; inertial method; nonexpansive mapping; strong convergence Halpern algorithm; viscosity algorithm; inertial method; nonexpansive mapping; strong convergence
MDPI and ACS Style

Tan, B.; Zhou, Z.; Li, S. Strong Convergence of Modified Inertial Mann Algorithms for Nonexpansive Mappings. Mathematics 2020, 8, 462.

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