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Mathematics
Volume 8
Issue 2
10.3390/math8020236
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Article

Modified Inertial Hybrid and Shrinking Projection Algorithms for Solving Fixed Point Problems

by
Bing Tan
1,
Shanshan Xu
2 and
Songxiao Li
1,*
1
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
2
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 236; https://doi.org/10.3390/math8020236
Submission received: 22 January 2020 / Revised: 9 February 2020 / Accepted: 10 February 2020 / Published: 12 February 2020
(This article belongs to the Special Issue Applied Functional Analysis and Its Applications)
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Abstract

In this paper, we introduce two modified inertial hybrid and shrinking projection algorithms for solving fixed point problems by combining the modified inertial Mann algorithm with the projection algorithm. We establish strong convergence theorems under certain suitable conditions. Finally, our algorithms are applied to convex feasibility problem, variational inequality problem, and location theory. The algorithms and results presented in this paper can summarize and unify corresponding results previously known in this field.
Keywords: conjugate gradient method; steepest descent method; hybrid projection; shrinking projection; inertial Mann; strongly convergence; nonexpansive mapping conjugate gradient method; steepest descent method; hybrid projection; shrinking projection; inertial Mann; strongly convergence; nonexpansive mapping

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MDPI and ACS Style

Tan, B.; Xu, S.; Li, S. Modified Inertial Hybrid and Shrinking Projection Algorithms for Solving Fixed Point Problems. Mathematics 2020, 8, 236. https://doi.org/10.3390/math8020236

AMA Style

Tan B, Xu S, Li S. Modified Inertial Hybrid and Shrinking Projection Algorithms for Solving Fixed Point Problems. Mathematics. 2020; 8(2):236. https://doi.org/10.3390/math8020236

Chicago/Turabian Style

Tan, Bing, Shanshan Xu, and Songxiao Li. 2020. "Modified Inertial Hybrid and Shrinking Projection Algorithms for Solving Fixed Point Problems" Mathematics 8, no. 2: 236. https://doi.org/10.3390/math8020236

APA Style

Tan, B., Xu, S., & Li, S. (2020). Modified Inertial Hybrid and Shrinking Projection Algorithms for Solving Fixed Point Problems. Mathematics, 8(2), 236. https://doi.org/10.3390/math8020236

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