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Continuity points and continuous selections of the set-valued metric generalized inverse in Banach spaces

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Abstract

In this paper, continuity points and continuous homogeneous selections of the set-valued metric generalized inverses T∂ in Banach spaces are investigated by means of the methods of geometry of Banach spaces. Moreover, the relation between continuity points and continuous homogeneous selection of the set-valued metric generalized inverse are given in approximatively compact Banach spaces. The results are an answer to the problem posed by Nashed and Votruba.

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Acknowledgement

This research is supported by “China Natural Science Fund” under grant 11871181 and 11561053.

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Authors and Affiliations

  1. College of Mathematical Sciences, Harbin Engineering University, Harbin, 150001, P. R. China

    Shaoqiang Shang

  2. Department of Mathematics, Harbin University of Science and Technology, Harbin, 150080, P. R. China

    Yunan Cui

Authors
  1. Shaoqiang Shang
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  2. Yunan Cui
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Correspondence to Shaoqiang Shang.

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Shang, S., Cui, Y. Continuity points and continuous selections of the set-valued metric generalized inverse in Banach spaces. Isr. J. Math. 234, 209–228 (2019). https://doi.org/10.1007/s11856-019-1917-z

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  • DOI: https://doi.org/10.1007/s11856-019-1917-z

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