Newton-cotes quadrature formula for third differentiable and h-convex functions

Key Points

• The aim is to develop a new Newton-Cotes quadrature formula tailored for third differentiable and h-convex functions.
• Introduced a new quadrature formula based on Newton-Cotes for specific functions.
• Utilized Riemann integrals in the formulation.
• Developed novel inequalities applicable to s-convexity and convexity.
• Demonstrated the efficacy of the new quadrature formula for integrating designated functions.
• Established new inequalities that enhance understanding of s-convexity and convexity.