On a half-discrete Hilbert-type inequality related to hyperbolic functions

Journal of inequalities and applications

Minghui You¹ 

[1] Mathematics Teaching and Research Section, Zhejiang Institute of Mechanical and Electrical Engineering, 310053, Hangzhou, China;

关键词: Hilbert-type inequality;    Half-discrete;    Bernoulli number;    Hyperbolic functions;    Rational fraction expansion;    26D15;    26D10;    47B38;   

DOI  :  10.1186/s13660-021-02688-7

来源: Springer

【 摘 要 】

By the introduction of a new half-discrete kernel which is composed of several exponent functions, and using the method of weight coefficient, a Hilbert-type inequality and its equivalent forms involving multiple parameters are established. In addition, it is proved that the constant factors of the newly obtained inequalities are the best possible. Furthermore, by the use of the rational fraction expansion of the tangent function and introducing the Bernoulli numbers, some interesting and special half-discrete Hilbert-type inequalities are presented at the end of the paper.

【 授权许可】

CC BY