Pointwise best coapproximation in the space of Bochner integrable functions

Eyad Abu-Sirhan

doi:10.33993/jnaat492-1206

Authors

Eyad Abu-Sirhan Tafila Technical University, Jordan https://orcid.org/0000-0003-1360-5554

DOI:

https://doi.org/10.33993/jnaat492-1206

Keywords:

best coapproximation , Coproximinal, Banach space.

Abstract views: 229

Abstract

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 $L^{p}(\mu,X$.

Downloads

Download data is not yet available.

References

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 in L∞(μ,X), International Journal of Mathematical Analysis,13(2019) no. 9, 449–458. https://doi.org/10.12988/ijma.2019.9847 DOI: https://doi.org/10.12988/ijma.2019.9847

H. Mazaheri, Jesmani, Some results on best coapproximation in L1(μ,X), Mediterr. J. Math., 4 (2007) no. 4, pp. 497–503. https://doi.org/10.1007/s00009-007-0131-0 DOI: https://doi.org/10.1007/s00009-007-0131-0

J. Jawdat, Best coapproximation in L∞(μ,X), TWMS J. App. Eng. Math., 8 (2018) no. 2, pp. 448–453

J. Mendoza, Proximinality in Lp(μ,X), J. Approx. Theory, 93 (1998), 331–343. https://doi.org/10.1006/jath.1997.3163 DOI: 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 best coapproximation in Lp(S,X), Anal. Theory Appl., 26 (2010) no. 1, 69–75. https://doi.org/10.1007/s10496-010-0069-0 DOI: 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 DOI: https://doi.org/10.1007/BF01305855

R. Khalil, Best approximation inLp(μ,X), Math. Proc. Cambridge Philos. Soc., 94 (1983), 277–279. https://doi.org/10.1017/s0305004100061120 DOI: https://doi.org/10.1017/S0305004100061120

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

W.A. Light, Proximinality in Lp(μ,X), Rocky Mountain J. Math., 19 (1989), 251–259, https://doi.org/10.1216/rmj-1989-19-1-251 DOI: https://doi.org/10.1216/RMJ-1989-19-1-251

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