# REMARKS ON REMOTAL SETS IN VETOR VALUED FUNCTION SPACES

Volume 2, Issue 1, pp 1-10
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### Authors

M. SABABHEH - Department of Science and Humanities, Princess Sumaya University For Technology, Al Jubaiha, Amman 11941, Jordan.. R. KHALIL - Department of Mathematics, Jordan University, Al Jubaiha, Amman 11942, Jordan..

### Abstract

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].

### Keywords

• Remotal sets
• Approximation theory in Banach spaces.

•  46B20
•  41A50
•  41A65

### References

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

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

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

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

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