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ISSN : 1226-0657

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Vol.12 No.3

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On Spherically Concave Functions

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2005, v.12 no.3, pp.229-235
KIM SEONG-A
KIM, S. (2005). On Spherically Concave Functions. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 12(3), 229-235.

Abstract

The notions of spherically concave functions defined on a subregion of the Riemann sphere P are introduced in different ways in Kim & Minda [The hyperbolic metric and spherically convex regions. J. Math. Kyoto Univ. 41 (2001), 297-314] and Kim & Sugawa [Charaterizations of hyperbolically convex regions. J. Math. Anal. Appl. 309 (2005), 37-51]. We show continuity of the concave function defined in the latter and show that the two notions of the concavity are equivalent for a function of class <TEX>$C^2$</TEX>. Moreover, we find more characterizations for spherically concave functions.

keywords
spherically concave function, spherical metric, hyperbolic metric

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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