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

DOI10.1090/PROC/16728arXiv2306.04659MaRDI QIDQ6439578

Publication date: 6 June 2023

Abstract: In this paper, we investigate the monotonicity of the functions

t m a p s t o f r a c s u m_{k = 0}^{i} n f t y a_{k} w_{k} (t) s u m_{k = 0}^{i} n f t y b_{k} w_{k} (t)

and

, focusing on case where the monotonicity of

a_{k} / b_{k}

and

f (t) / g (t)

change once. The results presented also provide insights into the monotonicity of the ratios of two power series, two

m a t h c a l Z

-transforms, two discrete Laplace transforms, two discrete Mellin transforms, two Laplace transforms, and two Mellin transforms. Finally, we employ these monotonicity rules to present several applications in the realm of special functions and stochastic orders.

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Laplace transform (44A10) Monotonic functions, generalizations (26A48) General integral transforms (44A05)