A systematization of convexity concepts for sets and functions.
Breckner, Wolfgang W., Kassay, Gábor (1997)
Journal of Convex Analysis
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Breckner, Wolfgang W., Kassay, Gábor (1997)
Journal of Convex Analysis
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Jacek Tabor, Józef Tabor, Krzysztof Misztal (2013)
Banach Center Publications
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There are many types of midconvexities, for example Jensen convexity, t-convexity, (s,t)-convexity. We provide a uniform framework for all the above mentioned midconvexities by considering a generalized middle-point map on an abstract space X. We show that we can define and study the basic convexity properties in this setting.
Marek Lassak (1982)
Colloquium Mathematicae
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Brzezina, Miroslav (1996)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Krzysztof Kołodziejczyk (1985)
Compositio Mathematica
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Bradford Hansen-Smith (2005)
Visual Mathematics
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Yong-Gao Chen, Min Tang (2012)
Acta Arithmetica
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V. Karunakaran, K. Bhuvaneswari (2007)
Colloquium Mathematicae
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Let 𝓐 denote the class of all analytic functions f in the open unit disc 𝔻 in the complex plane satisfying f(0) = 0, f'(0) = 1. Let U(λ) (0 < λ ≤ 1) denote the class of functions f ∈ 𝓐 for which |(z/f(z))²f'(z) -1| < λ for z ∈ 𝔻. The behaviour of functions in this class has been extensively studied in the literature. In this paper, we shall prove that no member of U₀(λ) = {f ∈ U(λ): f''(0) = 0} is convex in 𝔻 for any λ and obtain a lower bound...
Reza Sarhangi, Bruce D. Martin (2000)
Visual Mathematics
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W. L. Bynum (1972)
Compositio Mathematica
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Juan C. Bressan, Fausto A. Toranzos (1992)
Compositio Mathematica
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