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

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.

Submitted 25-Jul-2010; accepted 11-Nov-2010; to International Journal of Mathematics and Computation (IJMC)

References in corpus (6)

• Noether's Theorem on Time Scales
• Calculus of Variations on Time Scales with Nabla Derivatives
• Diamond-$\alpha$ Jensen's Inequality on Time Scales
• The diamond-alpha Riemann integral and mean value theorems on time scales
• Diamond-alpha Polynomial Series on Time Scales
• Diamond-alpha Integral Inequalities on Time Scales