Duality in vector optimization. III. Vector partially quasiconcave programming and vector fractional programming
Tran Quoc Chien (1984)
Kybernetika
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Tran Quoc Chien (1984)
Kybernetika
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Mohamed Sayed Ali Osman (1977)
Aplikace matematiky
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Zoltán Daróczy, Zsolt Páles (1987)
Stochastica
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Jain, O.P., Saxena, P.C. (1978)
Portugaliae mathematica
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O. Tikhonov (1993)
Studia Mathematica
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Let (A,e) and (V,K) be an order-unit space and a base-norm space in spectral duality, as in noncommutative spectral theory of Alfsen and Shultz. Let t be a norm lower semicontinuous trace on A, and let φ be a nonnegative convex function on ℝ. It is shown that the mapping a → t(φ(a)) is convex on A. Moreover, the mapping is shown to be nondecreasing if so is φ. Some other similar statements concerning traces and real-valued functions are also obtained.