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Journal of Function Spaces
Volume 2017, Article ID 7151430, 8 pages
https://doi.org/10.1155/2017/7151430
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.

Linked References

  1. M. Z. Nashed and G. F. Votruba, “A unified approach to generalized inverses of linear operators: II Extremal and proximinal properties,” Bulletin of the American Mathematical Society, vol. 80, pp. 831–835, 1974. View at Publisher · View at Google Scholar · View at MathSciNet
  2. S. Shang and Y. Cui, “Approximative compactness and continuity of the set-valued metric generalized inverse in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 422, no. 2, pp. 1363–1375, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. H. Hudzik, Y. Wang, and W. Zheng, “Criteria for the metric generalized inverse and its selections in Banach spaces,” Set-Valued Analysis. An International Journal Devoted to the Theory of Multifunctions and its Applications, vol. 16, no. 1, pp. 51–65, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. Y. Wang and J. Liu, “Metric generalized inverse for linear manifolds and extremal solutions of linear inclusion in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 302, no. 2, pp. 360–371, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. G. Chen and Y. Xue, “Perturbation analysis for the operator equation Tx=b in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 212, no. 1, pp. 107–125, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  6. Y. Wang and H. Zhang, “Perturbation analysis for oblique projection generalized inverses of closed linear operators in Banach spaces,” Linear Algebra and its Applications, vol. 426, no. 1, pp. 1–11, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. Y. W. Wang, Generalized Inverse of Operator in Banach Spaces and Applications, Science Press, Beijing, China, 2005.
  8. S. Shang and Y. Cui, “2-strict convexity and continuity of set-valued metric generalized inverse in Banach spaces,” Abstract and Applied Analysis, Article ID 384639, Art. ID 384639, 8 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. I. Singer, “On the set of the best approximations of an element in a normed linear space,” Romanian Journal of Pure and Applied Mathematics, vol. 5, no. 1, Article ID 383C402, 1960. View at Google Scholar
  10. N. W. Efimov and S. B. Stechkin, “Approximative compactness and chebyshev sets,” Soviet Mathematics—Doklady, vol. 2, no. 1, pp. 1226–1228, 1961. View at Google Scholar
  11. D. Nowakowska-Rozpłoch, “Set-Valued Analysis, Systems & Control Series, Vol. 2. By Jean-Paul Aubin and Hélène Frankowska, Birkhäuser, Boston, 1990,” Games and Economic Behavior, vol. 7, no. 3, pp. 473–475, 1994. View at Publisher · View at Google Scholar · View at Scopus
  12. S. Chen, H. Hudzik, W. Kowalewski, Y. Wang, and M. Wisła, “Approximative compactness and continuity of metric projector in Banach spaces and applications,” Science in China, Series A: Mathematics, vol. 51, no. 2, pp. 293–303, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus