Monotonicity rules for the ratio of two function series and two integral transforms

Zhong-Xuan Mao, Jing-Feng Tian

In this paper, we investigate the monotonicity of the functions $t\mapsto \frac{{\sum }_{k=0}^{\infty }{a}_k{w}_k(t)}{{\sum }_{k=0}^{\infty }{b}_k{w}_k(t)}$ and $x \mapsto \frac{\int_α^βf(t) w(t,…