TY - JOUR
T1 - Entanglement of Several Classical and Dynamic Estimates with Unified Approach on Time Scales
AU - Chaudhry , Faryal
AU - Sahir , Muhammad Jibril Shahab
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 1142
EP - 1152
PY - 2025
DA - 2025/07
SN - 7
DO - http://doi.org/10.12150/jnma.2025.1142
UR - https://global-sci.org/intro/article_detail/jnma/24229.html
KW - Time scales, fractional Riemann-Liouville integrals, Qi’s, Callebaut’s and Cauchy-Schwarz’s inequalities.
AB - <p style="text-align: justify;">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.</p>