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

Yıl 2018, Cilt: 1 Sayı: 2, 65 - 73, 31.08.2018

Yue Zhang Dingping Wu

Öz

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.

Anahtar Kelimeler

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

Kaynakça

  • [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

Yıl 2018, Cilt: 1 Sayı: 2, 65 - 73, 31.08.2018

Yue Zhang Dingping Wu

Öz

Kaynakça

  • [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
Toplam 7 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Yue Zhang Bu kişi benim

Dingping Wu Bu kişi benim

Yayımlanma Tarihi 31 Ağustos 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 1 Sayı: 2

Kaynak Göster

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. Ağustos 2018;1(2):65-73.
Chicago Zhang, Yue, ve Dingping Wu. “The Delta-convergence of proximal point iteration based on the variational inequality in CAT(0) Spaces”. Results in Nonlinear Analysis 1, sy. 2 (Ağustos 2018): 65-73.
EndNote Zhang Y, Wu D (01 Ağustos 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 ve D. Wu, “The Delta-convergence of proximal point iteration based on the variational inequality in CAT(0) Spaces”, RNA, c. 1, sy. 2, ss. 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 (Ağustos2018), 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 ve Dingping Wu. “The Delta-convergence of proximal point iteration based on the variational inequality in CAT(0) Spaces”. Results in Nonlinear Analysis, c. 1, sy. 2, 2018, ss. 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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