Аннотация:
Simpson-type inequalities are an important tool in mathematical analysis, particularly in the study of integrals. In this paper, we present new generalized $3/8$-Simpson-type inequalities for functions whose first derivative modulus is $(h, m)$-convex and satisfies the Lipschitz condition via weight integral operators. To obtain these results, we use a new integral identity established in our study. This research generalizes, extends, and complements the existing results in the literature.
Ключевые слова:
convex function, $(h, m)$-convex function, Simpson-type inequality, weighted integral operator, Hölder inequality, Power mean inequality, Young inequality, Lipschitz function.