Some monotonicity rules for quotient of integrals on time scales

2023/12/15 by Mao, Zhong-Xuan, Du, Xiao-Yue, Tian, Jing-Feng
#26A48 #26E70 #33B15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2312.10252

Abstract

As an efficient mathematical tool, monotonicity rules play an extremely crucial role in the real analysis field. In this paper, we explore some monotonicity rules for quotient of Delta, Nabla and Diamond-Alpha integrals with variable upper limits and parameters on time scales, respectively. Moreover, we consider the monotonicity rules for quotient of the product of multiple Delta integrals with parameters on time scales. Power series is also concerned for being a special case of integral with parameters on time scales.

Related

• Y-function and L'Hospital-type Monotonicity Rules with Nabla and Diamond-Alpha Derivatives on Time Scales
• Time scales: from Nabla calculus to Delta calculus and vice versa via duality
• Monotonicity rules for the ratio of two function series and two integral transforms
• Some inequalities for partial derivatives on time scales
• Generalized fraction rules for monotonicity with higher antiderivatives and derivatives