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Duality results involving functions associated to nonempty subsets of locally convex spaces

Resultados sobre dualidad mediante funciones asociadas a subconjuntos no vacios de espacios localmente convexos

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Abstract

In many papers on consumer theory and production analysis duality results between profit, revenue, cost, input, output and shortage functions are established. This functions are associated to certain subsets of ℝn. The aim of this paper is to study in a systematic way such duality results in locally convex spaces and to derive them under minimal hypotheses.

Resumen

En muchos artículos sobre teoría del consumo y análisis de la producción, se establecen resultados de dualidad entre beneficios y costes, e inversiones y rendimientos, proponiéndose diversas funciones de insuficiencia asociadas a ciertos subconjuntos de ℝn. El objeto de este trabajo es el estudio sistemático de dichos resultados de dualidad en espacios localmente convexos, y su obtención bajo condiciones mínimas.

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Correspondence to C. ZĂlinescu.

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ZĂlinescu, C. Duality results involving functions associated to nonempty subsets of locally convex spaces. Rev. R. Acad. Cien. Serie A. Mat. 103, 219–234 (2009). https://doi.org/10.1007/BF03191905

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Keywords

  • Duality results
  • localy convex spaces
  • shortage functions
  • profit
  • revenue
  • input
  • output

Mathematics Subject Classifications

  • 49N15
  • 90C46
  • 91B38