Pointwise best coapproximation in the space of Bochner integrable functions



best coapproximation , Coproximinal, Banach space.


Let \(X\) be a Banach space, \(G$\) be a closed subset of \(X\), and \((\Omega,\Sigma,\mu )\) be a \(\sigma\)-finite measure space. In this paper we present some results on coproximinality (pointwise coproximinality) of \(L^{p}(\mu,G)\), \(1\leq p\leq \infty\), in \(L^{p}(\mu,X\).


C. Franchetti, M. Furi,Some characteristic properties of real Hilbert spaces, Rev.Romaine Math. Pures Appl.,17(1972), 1045–1048.

E. Abu-Sirhan,A Remark on Best Coapproximation inL?(?,X), International Jour-nal of Mathematical Analysis,13(2019) no. 9, 449–458. https://doi.org/10.12988/ijma.2019.9847

H. Mazaheri, ? Jesmani,Some results on best coapproximation inL1(?,X), Mediterr.J. Math.,4(2007) no. 4, pp. 497–503. https://doi.org/10.1007/s00009-007-0131-0

J. Jawdat,Best coapproximation inL?(?,X),TWMS J. App. Eng. Math.,8(2018)no. 2, pp. 448–453

J. Mendoza,Proximinality inLp(?,X), J. Approx. Theory,93(1998), 331–343. https://doi.org/10.1006/jath.1997.3163

K. Kuratowiski, C. Ryll-Nardzewski,A general theorem on selector, Bull. Acad.Polonaise Science, Series Math. Astr. Phys.,13(1965), 379-403.

M. R. Haddadi, N. Hejazjpoor, H. Mazaheri,Some result about bestcoapproximation inLp(S,X),Anal. Theory Appl.,26(2010) no. 1, 69–75. https://doi.org/10.1007/s10496-010-0069-0

P.L. Papini, I. Singer,Best coapproximation in normed linear spaces, Mh. Math.,88(1979), 27–44. https://doi.org/10.1007/bf01305855

R. Khalil,Best approximation inLp(?,X), Math. Proc. Cambridge Philos. Soc.,94(1983), 277–279. https://doi.org/10.1017/s0305004100061120

R. Khalil, W. Deeb,Best approximation inLp(?,X), II, J. Approx. Theory,59(1989), 296–299. https://doi.org/10.1016/0021-9045(89)90094-4

W.A. Light,Proximinality inLp(?,X), Rocky Mountain J. Math.,19(1989), 251–259, https://doi.org/10.1216/rmj-1989-19-1-251

Y. Zhao-Yong, G. Tie-Xin,Pointwise best approximation in the space of strongly mea-surable functions with applications to best approximation inLp(?,X), J. Approx.Theory,78(1994), 314–320,https://doi.org/10.1006/jath.1994.1081




How to Cite

Abu-Sirhan, E. (2021). Pointwise best coapproximation in the space of Bochner integrable functions. J. Numer. Anal. Approx. Theory, 49(2), 95-99. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/1206