Study of new general integral results under original primitive-like inequality assumptions

Abstract

This article proposes new general inequalities based on the integral of two adaptive functions. The main originality of our results lies in two important aspects: (i) the assumptions considered, which combine monotonicity and primitive-like inequalities, and (ii) the expression of the bounds, where the power and logarithmic transformations play an important role. Several complementary integral inequalities are established under additional assumptions, including convexity assumptions. Applications and future directions are also discussed.