On the Extension of $q$-Hermite-Hadamard Inequalities for Strong Convexity (European Journal of Pure and Applied Mathematics, 2025)
This study leverages $q$-calculus to establish $q$-Hermite-Hadamard type inequalities for strongly convex functions, showcasing possible extensions of well-known results in the field. Additionally, it enhances these findings by exploring the strong convexity of the function $Φ$. Furthermore, the $q$-midpoint and $q$-trapezoidal inequalities are unified within a comprehensive framework. Ultimately, the results suggest that the newly derived inequalities can be effectively applied in the context of special means.
Keywords: H-H type inequalities, strongly convex functions, quantum calculus.