TY  - JOUR
T1  - The Delta-convergence of proximal point iteration based on the variational inequality in CAT(0) Spaces
AU  - Zhang, Yue
AU  - Wu, Dingping
PY  - 2018
DA  - August
JF  - Results in Nonlinear Analysis
JO  - RNA
PB  - Erdal KARAPINAR
WT  - DergiPark
SN  - 2636-7556
SP  - 65
EP  - 73
VL  - 1
IS  - 2
LA  - en
AB  - 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.
KW  - Mann-type
KW  - Ishikawa-type
KW  - variational inequality
KW  - nonexpansive mapping
KW  - Hadamard spaces
KW  - inexact
KW  - Delta-convergence
CR  - [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.
CR  - [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.
CR  - [3] Berg I D, Nikolaev I G. Quasilinearization and curvature of Aleksandrov spaces[J]. Geometriae Dedicata, 2008, 133(1):195-
218.
CR  - [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.
CR  - [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.
CR  - [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.
CR  - [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
UR  - https://dergipark.org.tr/en/pub/rna/issue//442725
L1  - https://dergipark.org.tr/en/download/article-file/504876
ER  -