Simultaneously proximinal subspaces

References

[1] Bandyopadhyay P. and Rao T. S. S. R. K., Central subspaces of Banach spaces, J. Approx. Theory 103 (2000), 206–222. 10.1006/jath.1999.3420Suche in Google Scholar

[2] Calder J. R., Coleman W. P. and Harris R. L., Centers of infinite bounded sets in a normed space, Canad. J. Math. 25 (1973), 986–999. 10.4153/CJM-1973-105-3Suche in Google Scholar

[3] Cheney E. W. and Wulbert D. E., The existence and unicity of best approximations, Math. Scand. 24 (1969), 113–140. 10.7146/math.scand.a-10925Suche in Google Scholar

[4] Dutta S. and Narayana D., Strongly proximinal subspaces of finite codimension in C⁢(K), Colloq. Math. 109 (2007), 119–128. 10.4064/cm109-1-10Suche in Google Scholar

[5] Indumathi V., Proximinal subspaces of finite codimension in direct sum spaces, Proc. Indian Acad. Sci. Math. Sci. 111 (2001), 229–239. 10.1007/BF02829593Suche in Google Scholar

[6] Jayanarayanan C. R. and Paul T., Strong proximinality and intersection properties of balls in Banach spaces, J. Math. Anal. Appl. 426 (2015), 1217–1231. 10.1016/j.jmaa.2015.01.013Suche in Google Scholar

[7] Lacey H. E., The Isometric Theory of Classical Banach Spaces, Grundlehren Math. Wiss. 208, Springer, Berlin, 1974. 10.1007/978-3-642-65762-7Suche in Google Scholar

[8] Light W. A. and Cheney E. W., Approximation Theory in Tensor Product Spaces, Lecture Notes in Mathematics 1169, Springer, Berlin, 1985. 10.1007/BFb0075391Suche in Google Scholar

[9] Lin P.-K., A remark on the sum of proximinal subspaces, J. Approx. Theory 58 (1989), 55–57. 10.1016/0021-9045(89)90007-5Suche in Google Scholar

[10] Mendoza J. and Pakhrou T., Best simultaneous approximation in L1⁢(μ,X), J. Approx. Theory 145 (2007), 212–220. 10.1016/j.jat.2006.09.003Suche in Google Scholar

[11] Rao T. S. S. R. K., Best constrained approximation in Banach spaces, Numer. Funct. Anal. Optim. 36 (2015), 248–255. 10.1080/01630563.2014.970274Suche in Google Scholar

[12] Rawashdeh M., Al-Sharif Sh. and Domi W. B., On the sum of best simultaneously proximinal subspaces, Hacet. J. Math. Stat. 43 (2014), 595–602. Suche in Google Scholar

[13] Saidi F. B., Hussein D. and Khalil R., Best simultaneous approximation in Lp⁢(I,E), J. Approx. Theory 116 (2002), 369–379. 10.1006/jath.2002.3676Suche in Google Scholar

[14] Singer I., Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces, Grundlehren Math. Wiss. 171, Springer, Berlin, 1970. 10.1007/978-3-662-41583-2Suche in Google Scholar

[15] Smith P. W. and Ward J. D., Restricted centers in C⁢(Ω), Proc. Amer. Math. Soc. 48 (1975), 165–172. 10.1090/S0002-9939-1975-0380227-3Suche in Google Scholar

[16] Veselý L., A Banach space in which all compact sets, but not all bounded sets, admit Chebyshev centers, Arch. Math. (Basel) 79 (2002), 499–506. 10.1007/BF02638387Suche in Google Scholar

[17] Veselý L., Chebyshev centers in hyperplanes of c0, Czechoslovak Math. J. 52(127) (2002), 721–729.10.1023/B:CMAJ.0000027227.85142.feSuche in Google Scholar