L'Hopital-Type Rules for Monotonicity with Application to Quantum Calculus

TL;DR

This paper develops new l'Hopital rules for monotonicity applicable on any time scale, including quantum calculus, and demonstrates their use in deriving bounds for exponential functions in quantum calculus.

Contribution

Introduces novel l'Hopital rules for monotonicity on arbitrary time scales, including quantum calculus, expanding the theoretical framework and applications.

Findings

Derived delta and nabla monotonic l'Hopital rules.

Established new bounds for exponential functions in quantum calculus.

Extended classical calculus results to quantum calculus context.

Abstract

We prove new l'Hopital rules for monotonicity valid on an arbitrary time scale. Both delta and nabla monotonic l'Hopital rules are obtained. As an example of application, we give some new upper and lower bounds for the exponential function of quantum calculus restricted to the q-scale.