Analysis of the Error Bounds in Numerical Integration for Log-Convex Functions

Abstract

This study aims to investigate the application of perturbed trapezoid inequalities in the numerical integration of n-times differentiable and logarithmically convex functions. The objective is to analyze the accuracy of numerical approximations, such as the trapezoidal and Simpson’s rules, by providing error bounds through these inequalities. By examining how these methods apply to logo-convex functions, the study presents suggestions into optimizing computational approaches and understanding the properties of these functions in various areas. The obtained findings are expected to contribute to the development of more precise and efficient in numerical integration techniques such as the rectangle, the trapezoid, and Simpson rule.

Keywords

• Convex functions
• log-convex functions
• Perturbed trapezoid inequality
• Numerical integration

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