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부등식의 대수, 해석, 기하학적 증명

노자영 (군산대학교 교육대학원)

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In this thesis we consider various inequalities such as arithmetic –geometric inequality and its weighted version, Cauchy-Schwarz inequality, rearrangement inequality, Chebyshev inequality, Carleman’s inequality and Holder inequality. In Section 1 we prove the inequalities using various algebraic ways(i.e., without using analytic tools such as continuity, differentiation, etc) and some exhibit some applications. In Section 3 we also give analytic proofs of the weighted arithmetic-geometric inequality and Holder inequality using various analytic ways such as basic calculus and Jensen inequality.
In this thesis we consider various inequalities such as arithmetic –geometric inequality and its weighted version, Cauchy-Schwarz inequality, rearrangement inequality, Chebyshev inequality, Carleman’s inequality and Holder inequality. In Section 1 we prove the inequalities using various algebraic ways(i.e., without using analytic tools such as continuity, differentiation, etc) and some exhibit some applications. In Section 3 we also give analytic proofs of the weighted arithmetic-geometric inequality and Holder inequality using various analytic ways such as basic calculus and Jensen inequality.