Work

Sharp bounds for Toader mean by arithmetic and centroidal means in exponential type with applications

Year: 2025

Type: article

Abstract: We establish the optimal lower and upper bounds for the Toader mean by arithmetic and centroidal means in exponential type. That is, for any fixed p ? R, we find the best possible parameters ? = ?(p) and ? = ?(p) such that ?p(a, b; ?) ? T(a, b) ? ?p(a, b; ?) are valid for all a, b > 0 with a ? b, where T(a, b) is the Toader mean of a and b, and ?p(a, b; ?) is the exponential type mean of a and b with ? ? (0, 1). As applications, several new sharp inequalities for the complete elliptic integral of the second kind will be derived.

Source: Applicable Analysis and Discrete Mathematics

DOI: 10.2298/aadm240529009l

Authors: Shan Li, Miao-Kun Wang, Xin-Hao Yu

Institution: Huzhou Normal University

Language: English

Topic: Mathematical Inequalities and Applications

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Natural Science Foundation of Zhejiang Province

Award: 超几何函数在两个几何问题中的应用研究