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Article

Generalized Viscosity Implicit Iterative Process for Asymptotically Non-Expansive Mappings in Banach Spaces

by
Chanjuan Pan
1 and
Yuanheng Wang
1,2,*
1
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
2
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(5), 379; https://doi.org/10.3390/math7050379
Submission received: 2 April 2019 / Revised: 21 April 2019 / Accepted: 23 April 2019 / Published: 26 April 2019
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications)
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Abstract

In this paper, we propose a generalized viscosity implicit iterative method for asymptotically non-expansive mappings in Banach spaces. The strong convergence theorem of this algorithm is proved, which solves the variational inequality problem. Moreover, we provide some applications to zero-point problems and equilibrium problems. Further, a numerical example is given to illustrate our convergence analysis. The results generalize and improve corresponding results in the literature.
Keywords: fixed point; variational inequality; generalized viscosity implicit rule; asymptotically nonexpansive mapping; Banach spaces fixed point; variational inequality; generalized viscosity implicit rule; asymptotically nonexpansive mapping; Banach spaces

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MDPI and ACS Style

Pan, C.; Wang, Y. Generalized Viscosity Implicit Iterative Process for Asymptotically Non-Expansive Mappings in Banach Spaces. Mathematics 2019, 7, 379. https://doi.org/10.3390/math7050379

AMA Style

Pan C, Wang Y. Generalized Viscosity Implicit Iterative Process for Asymptotically Non-Expansive Mappings in Banach Spaces. Mathematics. 2019; 7(5):379. https://doi.org/10.3390/math7050379

Chicago/Turabian Style

Pan, Chanjuan, and Yuanheng Wang. 2019. "Generalized Viscosity Implicit Iterative Process for Asymptotically Non-Expansive Mappings in Banach Spaces" Mathematics 7, no. 5: 379. https://doi.org/10.3390/math7050379

APA Style

Pan, C., & Wang, Y. (2019). Generalized Viscosity Implicit Iterative Process for Asymptotically Non-Expansive Mappings in Banach Spaces. Mathematics, 7(5), 379. https://doi.org/10.3390/math7050379

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