Convergence Theorems for Modified Inertial Viscosity Splitting Methods in Banach Spaces

Pan, Chanjuan; Wang, Yuanheng

doi:10.3390/math7020156

Open AccessArticle

Convergence Theorems for Modified Inertial Viscosity Splitting Methods in Banach Spaces

by

Chanjuan Pan

^† and

Yuanheng Wang

^*,†

Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China

^*

Author to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Mathematics 2019, 7(2), 156; https://doi.org/10.3390/math7020156

Submission received: 6 January 2019 / Revised: 28 January 2019 / Accepted: 30 January 2019 / Published: 8 February 2019

(This article belongs to the Special Issue Fixed Point, Optimization, and Applications)

Download

Browse Figure

Versions Notes

Abstract

In this article, we study a modified viscosity splitting method combined with inertial extrapolation for accretive operators in Banach spaces and then establish a strong convergence theorem for such iterations under some suitable assumptions on the sequences of parameters. As an application, we extend our main results to solve the convex minimization problem. Moreover, the numerical experiments are presented to support the feasibility and efficiency of the proposed method.

Keywords: Banach spaces; viscosity splitting method; inertial method; accretive operators

Share and Cite

MDPI and ACS Style

Pan, C.; Wang, Y. Convergence Theorems for Modified Inertial Viscosity Splitting Methods in Banach Spaces. Mathematics 2019, 7, 156. https://doi.org/10.3390/math7020156

AMA Style

Pan C, Wang Y. Convergence Theorems for Modified Inertial Viscosity Splitting Methods in Banach Spaces. Mathematics. 2019; 7(2):156. https://doi.org/10.3390/math7020156

Chicago/Turabian Style

Pan, Chanjuan, and Yuanheng Wang. 2019. "Convergence Theorems for Modified Inertial Viscosity Splitting Methods in Banach Spaces" Mathematics 7, no. 2: 156. https://doi.org/10.3390/math7020156

APA Style

Pan, C., & Wang, Y. (2019). Convergence Theorems for Modified Inertial Viscosity Splitting Methods in Banach Spaces. Mathematics, 7(2), 156. https://doi.org/10.3390/math7020156

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Menu

Convergence Theorems for Modified Inertial Viscosity Splitting Methods in Banach Spaces

Abstract

Share and Cite

Article Metrics

Article Access Statistics

Further Information

Guidelines

MDPI Initiatives

Follow MDPI