Displaying similar documents to “Hyperbolically convex functions II”

On uniformly convex functions

A. W. Goodman (1991)

Annales Polonici Mathematici

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We introduce a new class of normalized functions regular and univalent in the unit disk. These functions, called uniformly convex functions, are defined by a purely geometric property. We obtain a few theorems about this new class and we point out a number of open problems.

On some α -convex functions.

Acu, Mugur, Al-Oboudi, Fatima, Darus, Maslina, Owa, Shigeyoshi, Polatog̃lu, Yaşar, Yavuz, Emel (2008)

International Journal of Open Problems in Computer Science and Mathematics. IJOPCM

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A generalization of the Hahn-Banach theorem

Jolanta Plewnia (1993)

Annales Polonici Mathematici

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If C is a non-empty convex subset of a real linear space E, p: E → ℝ is a sublinear function and f:C → ℝ is concave and such that f ≤ p on C, then there exists a linear function g:E → ℝ such that g ≤ p on E and f ≤ g on C. In this result of Hirano, Komiya and Takahashi we replace the sublinearity of p by convexity.