A Fixed Point Iterative Method for Tensor Complementarity Problems

2020 ◽  
Vol 84 (3) ◽  
Author(s):  
Ping-Fan Dai
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Complementarity Problems ◽  
Tensor Complementarity ◽  
Tensor Complementarity Problems ◽  
Fixed Point Iterative Method

Stability of Solutions and Continuity of Solution Maps of Tensor Complementarity Problems

2019 ◽  
Vol 36 (02) ◽  
pp. 1940002 ◽  
Author(s):  
Xue-Li Bai ◽  
Zheng-Hai Huang ◽  
Xia Li
Keyword(s):  
Complementarity Problems ◽  
Stability Of Solutions ◽  
Uniqueness Of Solutions ◽  
Solution Maps ◽  
Upper Semicontinuous ◽  
Tensor Complementarity ◽  
Tensor Complementarity Problems ◽  
The Stability ◽  
The Relationship ◽  
Tensor Variational Inequality

Recently, tensor complementarity problems are becoming more and more popular. There are various literatures considering all kinds of properties of tensor complementarity problems, however, the stability of solutions and the continuity of solution maps are rarely mentioned so far. In the present paper, we study these two properties for tensor complementarity problems. We propose conditions under which the solutions of tensor complementarity problems are stable with the help of the tensor variational inequality or structured tensors. We also show that the solution maps of tensor complementarity problems are upper semicontinuous with the involved tensors being [Formula: see text]-tensors. Meanwhile, we establish the relationship between the uniqueness of solutions and the continuity of solution maps of tensor complementarity problems.

scholarly journals Approximating fixed points of demicontractive mappings by iterative methods defined as admissible perturbations

2016 ◽  
Vol 25 (1) ◽  
pp. 121-126
Author(s):  
CRISTINA TICALA ◽  
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Fixed Points ◽  
Iterative Methods ◽  
Hilbert Spaces ◽  
Convergence Theorems ◽  
Admissible Perturbation ◽  
Demicontractive Operator ◽  
Demicontractive Mappings ◽  
Fixed Point Iterative Method

The aim of this paper is to prove some convergence theorems for a general Krasnoselskij type fixed point iterative method defined by means of the concept of admissible perturbation of a demicontractive operator in Hilbert spaces.

Approximating fixed points of demicontractive mappings by iterative methods defined as admissible perturbations

2016 ◽  
Vol 25 (1) ◽  
pp. 121-126
Author(s):  
CRISTINA TICALA ◽  
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Fixed Points ◽  
Iterative Methods ◽  
Hilbert Spaces ◽  
Convergence Theorems ◽  
Admissible Perturbation ◽  
Demicontractive Operator ◽  
Demicontractive Mappings ◽  
Fixed Point Iterative Method

The aim of this paper is to prove some convergence theorems for a general Krasnoselskij type fixed point iterative method defined by means of the concept of admissible perturbation of a demicontractive operator in Hilbert spaces.

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