Some New Versions of Various Inequalities over Trapezoidal Fuzzy Codomain

Considerable attention has been given to Hölder's inequality, its extensions, and its reverse within the realms of differential equations and mathematical analysis. This study uses a new approach to find the novel version of Hölder's inequality by employing a fundamental analytical approach rooted in algebra and calculus known as trapezoidal fuzzy Hölder's inequality. With the help of Hölder's inequality, trapezoidal fuzzy Minkowski’s inequality and trapezoidal fuzzy Beckenbach’s inequality are also obtained. As specific examples of the inequalities mentioned earlier, our results illustrate various outcomes related to trapezoidal fuzzy Hölder's inequality. These outcomes show that the behavior of these inequalities is better than the classical results. For the validation of the results, some examples are also provided.