(untitled) (European Journal of Pure and Applied Mathematics, 2025)
This study presents weighted trapezoidal-type inequalities for the product of two functions. While one function takes its values in the Banach spaces, the other takes values in the complex plane. We employed the technique of integration by parts for Bochner integrals for functions of two variables, along with principles of analysis for functions taking values in the product of Banach spaces, to report our findings. In addition to the extension of previous studies on functions of a single variable, our work generalizes results reported in Dragomir for two functions whose product of their variables lies in Banach spaces. Our results are new and original since they do not yet exist in the literature.