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Ball proximinality of closed * subalgebras in C(Q)

V. Indumathi, S. Lalithambigai, Bor-Luh Lin (2007)

Extracta Mathematicae

The notion of ball proximinality and the strong ball proximinality were recently introduced in [2]. We prove that a closed * subalgebra A of C(Q) is strongly ball proximinal in C(Q) and the metric projection from C(Q), onto the closed unit ball of A, is Hausdorff metric continuous and hence has continuous selection.

Best approximation for nonconvex set in q -normed space

Hemant Kumar Nashine (2006)

Archivum Mathematicum

Some existence results on best approximation are proved without starshaped subset and affine mapping in the set up of q -normed space. First, we consider the closed subset and then weakly compact subsets for said purpose. Our results improve the result of Mukherjee and Som (Mukherjee, R. N., Som, T., A note on an application of a fixed point theorem in approximation theory, Indian J. Pure Appl. Math. 16(3) (1985), 243–244.) and Jungck and Sessa (Jungck, G., Sessa, S., Fixed point theorems in best...

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