New Estimation of Error in the Hadamard Inequality Pertaining to Coordinated Convex Functions in Quantum Calculus

Abstract

Convex bodies are symmetric in nature. Between the two variables of symmetry and convexity, a correlation connection is also perceptible. Due to the interchangeable analogous properties, the application on either of them has been practicable in these modern years. The current analysis sheds insight on a general new identity involving a number of parameters for a twice partial quantum differentiable function. We find several unique quantum integral inequalities by using the new identity and a twice partial quantum differentiable function whose absolute value is coordinated convex. In addition, we present several novel and interesting error estimation-like results related to the well-known quantum Hermite–Hadamard inequality. Some examples are provided at the end to support and demonstrate the effectiveness of the new outcomes.

Exploration of Quantum Milne–Mercer-Type Inequalities with Applications

“…Erden and Colleagues [23] investigated some error schemes of Simpson's second-type rules, applying the convexity property of the functions. Authors [24] computed some new error estimates of Hermite-Hadamard inequality in association with co-ordinated convex mappings over a rectangle. Jain et al [25] developed some new quantum variants of Saigo-type fractional operators and studied well-known inequalities by employing these operators.…”