Some Inequalities of Weddle'S Type for Coordinated Convex Functions With Their Applications and Numerical Analysis

In mathematical analysis and optimization, studying inequalities is crucial in advancing theoretical and practical applications. This paper delves into the intricate world of Weddle's type inequalities, specifically focusing on coordinated convex functions. Following a comprehensive study and understanding, this article establishes new inequalities of Weddle's type for coordinated convex functions. A new identity for Weddle's type of coordinated convex functions is introduced. Utilizing newly established Weddle's identity, error bounds for Weddle's rule on functions of two variables are proved. The results advance the theoretical understanding of Simpson's type inequalities for coordinated convex functions and offer practical insights into their optimization potential. Numerical examples and applications are provided to demonstrate the validity and importance of these results. These findings expand the mathematical analysis and optimization theoretical framework, offering practical tools for tackling real‐world problems with precision and efficiency.