Malaysian Journal of Mathematical Sciences, June 2026, Vol. 20, No. 2
Novel Estimates of Hermite-Hadamard Type Inequalities and Midpoint-like Results for Quantum Integrals
Nawaz T., Shahzad A.
Corresponding Email: tariqnawaz93@yahoo.com
Received date: 16 June 2025
Accepted date: 16 November 2025
Abstract:
In this study, using extended convex functions, we present and rigorously derive several new estimates of Hermite-Hadamard type inequalities in the context of quantum integrals. We apply power mean inequality and Hölder's inequality to extend these bounds further. As consequence of these results, we attain qmidpoint-like, Simpson's like, averaged midpoint-like, and trapezoid type results. In order to verify our presented results, we express those with the help of graphs by certain choices of parameters involved. In the end, to focus on utilization of the results, we offer two novel applications namely averaged midpoint-trapezoid-like and q-trapezoid like results of the produced results.
Keywords: Hadamard inequalities; midpoint-like results; quantum integrals.
