Opened Access Algunas desigualdades del analisis matemático
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Autor: Rico Domínguez, Esperanza Macarena
Director: Facenda Aguirre, José Antonio
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2017-06
Tipo de documento: Trabajo Fin de Grado
Titulación: Universidad de Sevilla. Grado en Matemáticas
Resumen: The comparison of quantities is an essential tool in mathematics. The art of inequalities is found in the clever, often subtle methods used to generate and verify them. The science of inequalities lies in their careful interpretation and in the knowledge of their scope and limitations. In this work we study some fundamental inequalities in mathematics. In the first chapter we prove the arithmetic - geometric mean inequality. A plenty of proofs of this inequality are known, induction, backward induction, use of Jensen inequality, swapping terms, use of Lagrange multiplier, convexity. We include the Cauchy original proof and another one due to Polya. We deal with convexity in second chapter. The Jensen inequality give us a new proof of the arithmetic - geometric mean inequality with arbitrary weights. Also, from the inequality of Young we derive the Holder inequality with positive weights. In the third chapter we study the behavior of weighted means of order p, including the extreme c...
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Tamaño: 2.241Mb
Formato: PDF


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