Article ID: MTJPAM-D-24-00042

Title: Alternative proofs of two mathematical propositions on two elementary functions


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-24-00042; Volume 7 / Issue 1 / Year 2025, Pages 10-16

Document Type: Research Paper

Author(s): ‪Feng Qi a‪, Bo-Yan Xi b

aSchool of Mathematics and Physics, Hulunbuir University, Hailar, Inner Mongolia, 021008, China – Retired researcher, 17709 Sabal Court, Dallas, TX 75252-8024, USA – School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo, Henan, 454010, China

bCollege of Mathematical Sciences, Inner Mongolia Minzu University, Tongliao, Inner Mongolia, 028043, China

Received: 1 April 2024, Accepted: 19 January 2025, Published: 7 May 2025

Corresponding Author: Feng Qi (Email address: qifeng618@gmail.com)

Full Text: PDF

Abstract

In the paper, with the aid of some properties of the extended mean values, the authors provide two alternative proofs of two lemmas employed in the paper (B.-Y. Xi and F. Qi, Necessary and sufficient conditions of Schur m-power convexity of a new mixed mean, Filomat 38 (19), 6937–6944, 2024).

Keywords: Extended mean value, integral representation, necessary and sufficient condition, alternative proof, decreasing property, inequality

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Cite this article

How to cite this article: F. Qi and B.-Y. Xi, Alternative proofs of two mathematical propositions on two elementary functions, Montes Taurus J. Pure Appl. Math. 7 (1), 10-16, 2025; Article ID: MTJPAM-D-24-00042.