Best p-Simultaneous Approximation in Some Metric Space

Let X be a Banach space, (I,m) be a finite measure space, and F be an increasing subadditive continuous function on [0,+\infty) with F(0)=0. In the present paper, we discuss the best p-simultaneous approximation of L\Phi(I,G) in L\Phi(I,X) where G is a closed subspace of X.

Anahtar Kelimeler:

Simultaneous, Approximation

Best p-Simultaneous Approximation in Some Metric Space

Keywords:

Simultaneous, Approximation,

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Alsharif, sh.: Best Simultaneous Approximation LΦ(I , X ), submitted. Chong, L., and Watson, G. A: On the Best Simultaneously Approximation, J. Approx. Theory, 91, 332-348(1997).
Deeb, W. and Khalil, R.: On the Tensor Product of Non Locally Topological Vector Spaces, Illinois J. Math. Proc. 30,594-601(1986).
Deeb, W. and Khalil, R.: Best Approximation in Lp(I , X ), 0 < p < 1, J. Approx. Theory, , 68-77(1989).
Deeb, W. an d Youn is, Y.: Extreme Points in a Class of Non Locally Convex Topological vector space,Math. Reb. Toyama Univ. 6, 95-103(1983, New York (1972).
Khalil, R and Saidi, F.: Best Approximation in L1(I , X ), Proc. Amer. Math. Soc., 123, 190 (1995).
Mach, J.: Best Simultanneous Approximation of Vector Valued Function with Values in Certain Banach Spaces, Math. Ann, 240, 157-164 (1979).
Milman, P. D.: On Best Simultaneous Approximation in Normed Linear Spaces, J. Approx. Theory, 20, 223-238 (1977).
Pinkus, A.: Uniqueneness in Vector Valued Approxomation, J. Approx. Theory, 73, 17-92 (1993).
Sahn ey, B. N., an d Sin gh, S. P.: On Best Simultaneous Approximation in Banach Spaces, J. Approx. Theory, 35, 222-224 (1982).
Saidi, F., Hussein, D. and Khalil, R.: Best Simultaneous Approximation in Lp(I , X ), J. ApproximationTheory, 116, 369-379 (2002).
Tanimoto, S.: On the Best Simultaneous Approximation, Math. Japonica, 48, 275-279 (1998).
Watson, G. A.:A Characterization of Best Simultaneous Approximation, J. Approx. Theory, 75, 175-182 (1993).
M. KHANDAQJI, W. SHATANAWI Department of Mathematics The Hashemite University Zarqa-JORDAN email: mkhan@hu.edu.jo• swasŞ@hu.edu.jo