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Optimization Letters

, Volume 12, Issue 1, pp 87–102

# Modified inertial Mann algorithm and inertial CQ-algorithm for nonexpansive mappings

Original Paper

## Abstract

In this article, we first introduce a modified inertial Mann algorithm and an inertial CQ-algorithm by combining the accelerated Mann algorithm and the CQ-algorithm with the inertial extrapolation, respectively. This strategy is intended to speed up the convergence of the given algorithms. Then we established the convergence theorems for two provided algorithms. For the inertial CQ-algorithm, the conditions on the inertial parameters are very weak. Finally, the numerical experiments are presented to illustrate that the modified inertial Mann algorithm and inertial CQ-algorithm may have a number of advantages over other methods in computing for some cases.

## Keywords

Nonexpansive mapping Inertial extrapolation CQ-algorithm The inertial Mann algorithm Mann algorithm The accelerated Mann algorithm

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## Copyright information

© Springer-Verlag Berlin Heidelberg 2016

## Authors and Affiliations

• Q. L. Dong
• 1
• 2
• H. B. Yuan
• 1
• Y. J. Cho
• 3
• 4
Email author
• Th. M. Rassias
• 5
1. 1.College of ScienceCivil Aviation University of ChinaTianjinChina
2. 2.Tianjin Key Lab for Advanced Signal ProcessingCivil Aviation University of ChinaTianjinChina
3. 3.Department of Mathematics Education and RINSGyeongsang National UniversityJinjuKorea
4. 4.Center for General EducationChina Medical UniversityTaichungTaiwan
5. 5.Department of MathematicsNational Technical University of AthensAthensGreece

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