Some Novelty Quantum Hermite-Hadamard Type Inequalities Pertaining To Coordinated (s,t)-Convex Functions

Convexity assumptions play an important role in mathematical analysis. In this work, we establish a midpoint-type inequality for the average value of (s,t)-convex functions of the second kind within the framework of quantum calculus. We begin by presenting a new identity for functions that are twice partially quantum differentiable. Using this identity, we derive two inequalities that provide error estimates for a generalized Hadamard inequality. We also demonstrate how these results apply to continuous functions whose second-order quantum partial derivatives are (s,t)-convex of the second kind in absolute value. Graphical examples are included to illustrate and compare the results. Finally, we present applications involving special means of positive real numbers.

کلیدواژه ها:

Hermite-Hadamard inequality ، Coordinated convex functions ، Twice partially quantum derivatives ، Quantum double integrals ، power-mean inequality ، Special means