Sharp Generalized Inequalities for Certain Finite Products Derived From Complete Monotonicity and the Gamma Function

Jenică Crînganu

Journal of Mathematics, 2026, vol. 2026, 1-5

Abstract: In this paper, we establish a unified approach of inequalities for the finite products i⋅i+k⋅⋅⋅i+n−1k/k⋅2k⋅⋅⋅nk, where k≥2 is a fixed integer and i∈1,2,…,k−1. Motivated by previously known results for the cases k=2,3,4, and 5, we express these products in terms of gamma function ratios and investigate the complete monotonicity of a corresponding family of auxiliary functions. As a consequence, we obtain sharp lower and upper bounds with the best possible constants. The obtained theorem provides a unified approach for all previously known cases and establishes new inequalities for every integer k≥2

Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2026/5073580.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2026/5073580.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:5073580

DOI: 10.1155/jom/5073580

Access Statistics for this article

More articles in Journal of Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().