Pointwise coproximinality in \(L^p(\mu, X)\)
DOI:
https://doi.org/10.33993/jnaat521-1328Keywords:
Best coapproximation, coproximinal, Banach spaceAbstract
Let \(X\) be a Banach space, \(G\) be a closed subspace of \(X\), \((\Omega,\Sigma,\mu)\) be a \(\sigma\)-finite measure space, \(L(\mu,X)\) be the space of all strongly measurable functions from \(\Omega\) to \(X\), and \(L^{p}(\mu,X)\) be the space of all Bochner \(p-\)integrable functions from \(\Omega\) to \(X\).
Discussing the relationship between the pointwise coproximinality of \(L(\mu, G)\) in \(L(\mu, X)\) and the pointwise coproximinality of \(L^{p}(\mu, G)\) in \(L^{p}(\mu, X)\) is the purpose of this paper.
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E. Abu-Sirhan, A Remark on Best Coapproximation in L∞(μ, X), Intern. J. Math. Anal., 13 (2019), https://doi.org/10.12988/ijma.2019.9847), pp. 449–458. DOI: https://doi.org/10.12988/ijma.2019.9847
E. Abu-Sirhan, Pointwise Best Coapproximation in the Space of Bochner Inte- grable Functions, Journal of Numerical Analysis and Approximation Theory, 49 (2020),https://doi.org/10.33993/jnaat492-1206), pp. 95–99. DOI: https://doi.org/10.33993/jnaat492-1206
J. Diestel and J. Uhl, Vector Measures, vol. 15 of Mathematical Surveys, American Mathematical Society, Providence, RI, USA, (1977), https: dx.doi.org/10.1090/surv/015). DOI: https://doi.org/10.1090/surv/015
C. Franchetti and M. Furi, Some Characteristic Properties of Real Hilbert Spaces, Rev. Roumaine Math. Pures Appl, 17 (1972), pp. 1045–1048.
M. Haddadi, N. Hejazjpoor, and H. Mazaheri, Some Results about Best Coapproximation in Lp(μ, X), Analysis in Theory and Applications, 26 (2010), pp. 69–75. DOI: https://doi.org/10.1007/s10496-010-0069-0
J. Jawdat, Best Coapproximation in L∞(μ, X), Journal of Applied and Engineering Mathematics, 8 (2018), pp. 448–454.
H. Mazaheri and S. J. Jesmani, Some Results on Best Coapproximation in L1(μ, X), Mediterranean Journal of Mathematics, 4 (2007), pp. 497–503. DOI: https://doi.org/10.1007/s00009-007-0131-0
P. L. Papini and I. Singer, Best Coapproximation in Normed Linear Spaces, Monat shefte f ̈ur Mathematik, 88 (1979), pp. 27–44. DOI: https://doi.org/10.1007/BF01305855
G. Tie-Xin and Y. Zhao-Yong, Pointwise Best Approximation in the Space of Strongly Measurable Functions with Applications to Best Approximation in Lp(μ, X), Journal of Approximation Theory, 78 (1994 publisher- Elsevier), pp. 314–320, https://doi.org/10.1006/jath.1994.1081 DOI: https://doi.org/10.1006/jath.1994.1081
G. Tie-Xin and Y. Zhao-Yong, A note on pointwise best approximation, Journal of approximation theory, 93 (1998 https://doi.org/10.1006/jath.1997.3173 publisher-Academic Press), pp. 344–347. DOI: https://doi.org/10.1006/jath.1997.3173
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