EN
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] 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] 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] Berg I D, Nikolaev I G. Quasilinearization and curvature of Aleksandrov spaces[J]. Geometriae Dedicata, 2008, 133(1):195- 218.
- [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] 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] 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] 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
Publication Date
August 31, 2018
Submission Date
May 15, 2018
Acceptance Date
June 24, 2018
Published in Issue
Year 2018 Volume: 1 Number: 2
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