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2000•Mathematical Inequalities & ApplicationsOpen access

New proofs of weighted power mean inequalities and monotonicity for generalized weighted mean values

Feng Xiao Qi, Jia-Qiang Mei, Da-Feng Xia, Sen-Lin Xu

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Abstract

In the article, a new proof of the weighted power mean inequalities is given using Cauchy-Schwarz-Buniakowski's inequality, and another two simple and short proofs of monotonicity for the generalized weighted mean values with two parameters are showed.

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What this paper is about

In the article, a new proof of the weighted power mean inequalities is given using Cauchy-Schwarz-Buniakowski's inequality, and another two simple and short proofs of monotonicity for the generalized weighted mean values with two parameters are showed.

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OpenAlex reports 29 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In the article, a new proof of the weighted power mean inequalities is given using Cauchy-Schwarz-Buniakowski's inequality, and another two simple and short proofs of monotonicity for the generalized weighted mean values with two parameters are showed.

Key concepts: Mathematics, Monotonic function, Mathematical proof, Weighted arithmetic mean, Inequality, Generalized mean, Power (physics), Pure mathematics

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