Almost convexity and continuous selections of the set-valued metric generalized inverse in Banach spaces

2020 ◽  
Vol 15 (1) ◽  
Author(s):  
Shaoqiang Shang ◽  
Yunan Cui
Keyword(s):  
Banach Spaces ◽  
Generalized Inverse ◽  
Continuous Selections ◽  
Almost Convexity ◽  
Metric Generalized Inverse

Criteria for the Metric Generalized Inverse and its Selections in Banach Spaces

2007 ◽  
Vol 16 (1) ◽  
pp. 51-65 ◽  
Author(s):  
Henryk Hudzik ◽  
Yuwen Wang ◽  
Wenjing Zheng
Keyword(s):  
Banach Spaces ◽  
Generalized Inverse ◽  
Metric Generalized Inverse

scholarly journals Perturbation bounds for the metric projection of a point onto a linear manifold in reflexive strictly convex Banach spaces

Filomat ◽  
2018 ◽  
Vol 32 (19) ◽  
pp. 6829-6836
Author(s):  
Jianbing Cao ◽  
Hongwei Jiao
Keyword(s):  
Banach Spaces ◽  
Generalized Inverse ◽  
Linear Manifold ◽  
Metric Projection ◽  
Operator Equations ◽  
Perturbation Bounds ◽  
Strictly Convex ◽  
Ill Posed ◽  
Strictly Convex Banach Spaces ◽  
Metric Generalized Inverse

In this paper, by using some recent perturbation bounds for the Moore-Penrose metric generalized inverse, we present some results on the perturbation analysis for projecting a point onto a linear manifold in reflexive strictly convex Banach spaces. The main results have two parts, part one covers consistent operator equations and part two covers the general so-called ill posed operator equations.

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