Research Article

The Delta-convergence of proximal point iteration based on the variational inequality in CAT(0) Spaces

Volume: 1 Number: 2 August 31, 2018
  • Yue Zhang
  • Dingping Wu
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Results in Nonlinear Analysis
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The Delta-convergence of proximal point iteration based on the variational inequality in CAT(0) Spaces

Abstract

In this paper, we build the inexact proximal point algorithm of Mann-type and Ishikawa-type iteration based on the variational inequality in Hadamard spaces and prove Delta-convergence to a fixed point of the nonexpansive mapping.

Keywords

References

  1. [1] Kirk W A, Panyanak B. A concept of convergence in geodesic spaces[J]. Nonlinear Analysis Theory Methods and Applica- tions, 2008, 68(12):3689-3696.
  2. [2] Khatibzadeh H, Ranjbar S. A variational inequality in complete CAT(0) spaces[J]. Journal of Fixed Point Theory and Applications, 2015, 17(3):557-574.
  3. [3] Berg I D, Nikolaev I G. Quasilinearization and curvature of Aleksandrov spaces[J]. Geometriae Dedicata, 2008, 133(1):195- 218.
  4. [4] S. Dhompongsa, B. Panyanak. On ąœ-convergence theorems in CAT(0) spaces[J]. Computers And Mathematics with Ap- plications, 2008, 56(10):2572-2579.
  5. [5] Ranjbar S, Khatibzadeh H. Delta-CONVERGENCE AND W-CONVERGENCE OF THE MODIFIED MANN ITERATION FOR A FAMILY OF ASYMPTOTICALLY NONEXPANSIVE TYPE MAPPINGS IN COMPLETE CAT(0) SPACES[J]. International Journal on Fixed Point Theory Computation And Applications, 2016, 17(1):151-158.
  6. [6] Zeng L C. A Note on Approximating Fixed Points of Nonexpansive Mappings by the Ishikawa Iteration Process ąî[J]. Journal of Mathematical Analysis and Applications, 1998, 178(2):245-250.
  7. [7] Kirk W A, Panyanak B. A concept of convergence in geodesic spaces[J]. Nonlinear Analysis-Theory Methods and Applica- tions, 2008, 68(12):3689-3696

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Yue Zhang This is me
China

Dingping Wu This is me
China

Publication Date

August 31, 2018

Submission Date

May 15, 2018

Acceptance Date

June 24, 2018

Published in Issue

Year 2018 Volume: 1 Number: 2

IZ

https://izlik.org/JA84GN36AD

Cite

RIS / Bibtex
APA
Zhang, Y., & Wu, D. (2018). The Delta-convergence of proximal point iteration based on the variational inequality in CAT(0) Spaces. Results in Nonlinear Analysis, 1(2), 65-73. https://izlik.org/JA84GN36AD
AMA
1.Zhang Y, Wu D. The Delta-convergence of proximal point iteration based on the variational inequality in CAT(0) Spaces. RNA. 2018;1(2):65-73. https://izlik.org/JA84GN36AD
Chicago
Zhang, Yue, and Dingping Wu. 2018. “The Delta-Convergence of Proximal Point Iteration Based on the Variational Inequality in CAT(0) Spaces”. Results in Nonlinear Analysis 1 (2): 65-73. https://izlik.org/JA84GN36AD.
EndNote
Zhang Y, Wu D (August 1, 2018) The Delta-convergence of proximal point iteration based on the variational inequality in CAT(0) Spaces. Results in Nonlinear Analysis 1 2 65–73.
IEEE
[1]Y. Zhang and D. Wu, “The Delta-convergence of proximal point iteration based on the variational inequality in CAT(0) Spaces”, RNA, vol. 1, no. 2, pp. 65–73, Aug. 2018, [Online]. Available: https://izlik.org/JA84GN36AD
ISNAD
Zhang, Yue - Wu, Dingping. “The Delta-Convergence of Proximal Point Iteration Based on the Variational Inequality in CAT(0) Spaces”. Results in Nonlinear Analysis 1/2 (August 1, 2018): 65-73. https://izlik.org/JA84GN36AD.
JAMA
1.Zhang Y, Wu D. The Delta-convergence of proximal point iteration based on the variational inequality in CAT(0) Spaces. RNA. 2018;1:65–73.
MLA
Zhang, Yue, and Dingping Wu. “The Delta-Convergence of Proximal Point Iteration Based on the Variational Inequality in CAT(0) Spaces”. Results in Nonlinear Analysis, vol. 1, no. 2, Aug. 2018, pp. 65-73, https://izlik.org/JA84GN36AD.
Vancouver
1.Yue Zhang, Dingping Wu. The Delta-convergence of proximal point iteration based on the variational inequality in CAT(0) Spaces. RNA [Internet]. 2018 Aug. 1;1(2):65-73. Available from: https://izlik.org/JA84GN36AD