Essays about: "inequality of arithmetic and geometric means"

Found 2 essays containing the words inequality of arithmetic and geometric means.

1. 1. Complex Multiplicative Calculus and Mixed Problems

   University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten)

   Author : Axel Lokrantz; [2022]
   Keywords : multiplicative integrals; multiplicative calculus; product integrals; geometric mean; continuous geometric mean; geometric mean of non-negative random variables; inequality of arithmetic and geometric means; A_G-G_A inequality; generalized Hölder s inequality; multiplicative vector spaces; multiplicative function spaces; exponential transition functor; logarithmic Riemann surface; lift; function lift; projection; function projection; lift-projection method; multivalued complex multiplicative integrals; geometric expectation; mixed differential equation; Lambert W function; W; M; w and m functions; Mathematics and Statistics;

   Abstract : In this thesis we consider multiplicative integrals and derivatives on functions on the positive numbers, the logarithmic Riemann surface and the punctured complex numbers. Additive structures on the real and complex numbers are related to their multiplicative counterparts on the positive numbers and the logarithmic Riemann surface by defining exponential transition functors. READ MORE

3. 2. The Cauchy-Schwarz inequality : Proofs and applications in various spaces

   University essay from Karlstads universitet/Avdelningen för matematik

   Author : Thomas Wigren; [2015]
   Keywords : Cauchy-Schwarz inequality; mathematical induction; triangle inequality; Pythagorean theorem; arithmetic-geometric means inequality; inner product space;

   Abstract : We give some background information about the Cauchy-Schwarz inequality including its history. We then continue by providing a number of proofs for the inequality in its classical form using various proof techniques, including proofs without words. READ MORE