Open AccessA Hardy-Hilbert-type inequality involving modified weight coefficients and partial sums
Author(s) -
Xianyong Huang,
AUTHOR_ID,
Shanhe Wu,
Bicheng Yang,
AUTHOR_ID,
AUTHOR_ID
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022350
Subject(s) - mathematics , inequality , operator (biology) , log sum inequality , kantorovich inequality , type (biology) , hilbert space , rearrangement inequality , cauchy–schwarz inequality , pure mathematics , bessel's inequality , constant (computer programming) , linear inequality , mathematical analysis , computer science , ecology , biochemistry , chemistry , repressor , biology , transcription factor , gene , programming language
In this article, we construct proper weight coefficients and use them to establish a Hardy-Hilbert-type inequality involving one partial sum. Based on this inequality, the equivalent conditions of the best possible constant factor related to several parameters are discussed. We also consider the equivalent forms and the operator expressions of the obtained inequalities. At the end of the paper, we demonstrate that more new Hardy-Hilbert-type inequalities can be derived from the special cases of the present results.