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

Year 2018, Volume: 1 Issue: 2, 65 - 73, 31.08.2018

Yue Zhang Dingping Wu

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

Mann-type Ishikawa-type variational inequality nonexpansive mapping Hadamard spaces inexact Delta-convergence

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

Year 2018, Volume: 1 Issue: 2, 65 - 73, 31.08.2018

Yue Zhang Dingping Wu

Abstract

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
There are 7 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Yue Zhang This is me

Dingping Wu This is me

Publication Date August 31, 2018
Published in Issue Year 2018 Volume: 1 Issue: 2

Cite

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.
AMA Zhang Y, Wu D. The Delta-convergence of proximal point iteration based on the variational inequality in CAT(0) Spaces. RNA. August 2018;1(2):65-73.
Chicago 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 1, no. 2 (August 2018): 65-73.
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 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, 2018.
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 2018), 65-73.
JAMA 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, 2018, pp. 65-73.
Vancouver 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.
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