Entanglement of Several Classical and Dynamic Estimates with Unified Approach on Time Scales

Abstract

In this research article, we present several generalizations of Qi’s inequality on time scales. We establish dynamic versions of Callebaut’s inequality and Cauchy-Schwarz’s inequality on time scales. To establish our results, we apply the diamond-alpha integral and the time scale $∆$ or $∇$-Riemann-Liouville type fractional integrals. Our findings unify and extend discrete, continuous and quantum analogues.