• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1363-1372
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• 2007

We investigate the containment measure of one domain to contain in another domain in a plane $X^{\kappa}$ of constant curvature. We obtain some Bonnesen-type inequalities involving the area, length, radius of the inscribed and the circumscribed disc of a domain D in $X^{\kappa}$.