Araştırma Makalesi
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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 Araştırma Makalesi
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.