Geodesic
REMARKS ON REMOTAL SETS IN VETOR VALUED FUNCTION SPACES
SABABHEH , M. 1 ; KHALIL, R.2
1 Department of Science and Humanities, Princess Sumaya University For Technology, Al Jubaiha, Amman 11941, Jordan.
2 Department of Mathematics, Jordan University, Al Jubaiha, Amman 11942, Jordan.
Journal of nonlinear sciences and its applications, Tome 2 (2009) no. 1, p. 1-10.

Voir la notice de l'article provenant de la source International Scientific Research Publications

Let $X$ be a Banach space and $E$ be a closed bounded subset of $X$. For $x \in X$ we set $D(x,E) = \sup\{\| x − e \|: e \in E\}$. The set $E$ is called remotal in $X$ if for any $x \in X$, there exists $e \in E$ such that $D(x,E) = \| x − e \|$ . It is the object of this paper to give new results on remotal sets in $L^p(I,X)$, and to simplify the proofs of some results in [5].
DOI : 10.22436/jnsa.002.01.01
Classification : 46B20, 41A50, 41A65
Keywords: Remotal sets, Approximation theory in Banach spaces.

SABABHEH , M.  1 ; KHALIL, R. 2

1 Department of Science and Humanities, Princess Sumaya University For Technology, Al Jubaiha, Amman 11941, Jordan.
2 Department of Mathematics, Jordan University, Al Jubaiha, Amman 11942, Jordan. 
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SABABHEH , M. ; KHALIL,  R. REMARKS ON REMOTAL SETS IN VETOR VALUED FUNCTION SPACES. Journal of nonlinear sciences and its applications, Tome 2 (2009) no. 1, p. 1-10. doi : 10.22436/jnsa.002.01.01. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.002.01.01/

[1] Asplund, E. Farthest points in reflexive locally uniformly rotund Banach spaces, Israel J. Math. , Volume 4 (1966), pp. 213-216

[2] Baronti, M.; Papini, P. Remotal sets revisited, Taiwanese J. Math., Volume 5 (2001), pp. 357-373

[3] Boszany, A. A remark on uniquely remotal sets in C(K,X) , Period.Math.Hungar, Volume 12 (1981), pp. 11-14

[4] Cheney, E.; W. Light Lecture notes in Mathematics, Springer-Verlag Berlin Heidelberg, , 1985

[5] Khalil, R.; Al-Sharif, Sh. Remotal sets in vector valued function spaces, Scientiae Mathematicae Japonica, 63, No, Volume 3 (2006), pp. 433-441

[6] Rolewicz, S. Functional analysis and control theory, D.Reidel publishing company, , 1986.

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