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Journal of Function Spaces
Volume 2017, Article ID 7151430, 8 pages
Research Article

Metric Projection Operator and Continuity of the Set-Valued Metric Generalized Inverse in Banach Spaces

1Department of Mathematics, Northeast Forestry University, Harbin 150040, China
2Department of Mathematics and Applied Mathematics, Harbin University of Commerce, Harbin 150028, China

Correspondence should be addressed to Shaoqiang Shang; moc.361@gnahsqs

Received 17 April 2017; Accepted 28 June 2017; Published 31 July 2017

Academic Editor: Hugo Leiva

Copyright © 2017 Shaoqiang Shang and Jingxin Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper, continuous homogeneous selection and continuity for the set-valued metric generalized inverses in 3-strictly convex spaces are investigated by continuity of metric projection. The results are an answer to the problem posed by Nashed and Votruba. Moreover, authors prove that there exists a proximinal hyperplane such that is continuous and is not approximative compact.