Quantum Maclaurin-type inequalities for q-differentiable convex functions and their applications

F. Aissaoui, N. Nasri, A. Küçükaslan, J. Alzabut and Badreddine Meftah

This study presents novel quantum analogs of Maclaurin-type inequalities for functions possessing convex q-derivatives. We present and validate the principal results by obtaining a new quantum integral identity. Furthermore, we utilize these inequalities to establish error bounds for the Maclaurin quadrature formula and for specific means, including arithmetic and p-logarithmic means, therefore illustrating their importance in mathematical analysis. The conclusions gained not only generalize current inequalities but also establish a foundation for further investigation in integral inequalities and their quantum counterparts. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 19(1) (2026), pp. 143-165