Quasi-convexity, strictly quasi-convexity and pseudo-convexity of composite objective functions
Bernard Bereanu (1972)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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Bernard Bereanu (1972)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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M. Emin Özdemir, Ahmet Ocak Akdemir, Çetin Yıldız (2012)
Czechoslovak Mathematical Journal
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A function , where is an interval, is said to be a convex function on if holds for all and . There are several papers in the literature which discuss properties of convexity and contain integral inequalities. Furthermore, new classes of convex functions have been introduced in order to generalize the results and to obtain new estimations. We define some new classes of convex functions that we name quasi-convex, Jensen-convex, Wright-convex, Jensen-quasi-convex and Wright-quasi-convex...
Wang, Zhi-Gang (2006)
Lobachevskii Journal of Mathematics
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Wang, Zhi-Gang, Chen, Hui (2007)
Lobachevskii Journal of Mathematics
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Looney, Carl G. (1978)
International Journal of Mathematics and Mathematical Sciences
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Syau, Yu-Ru (1999)
International Journal of Mathematics and Mathematical Sciences
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Malivert, C., Boissard, N. (1994)
Journal of Convex Analysis
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Ignacio Monterde, Vicente Montesinos (2008)
Studia Mathematica
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A single technique provides short proofs of some results about drop properties on locally convex spaces. It is shown that the quasi drop property is equivalent to a drop property for countably closed sets. As a byproduct, we prove that the drop and quasi drop properties are separably determined.
Levin, Vladimir L. (1995)
Journal of Convex Analysis
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J. H. Qiu (2003)
Studia Mathematica
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Every weakly sequentially compact convex set in a locally convex space has the weak drop property and every weakly compact convex set has the quasi-weak drop property. An example shows that the quasi-weak drop property is strictly weaker than the weak drop property for closed bounded convex sets in locally convex spaces (even when the spaces are quasi-complete). For closed bounded convex subsets of quasi-complete locally convex spaces, the quasi-weak drop property is equivalent to weak...
Bella Tsirulnikov (1981)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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