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New Means of Cauchy's Type

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Abstract

We will introduce new means of Cauchy's type defined, for example, as in the case when , . We will show that this new Cauchy's mean is monotonic, that is, the following result. Theorem. Let , such that , . Then for , one has . We will also give some related comparison results.

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Correspondence to Matloob Anwar.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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