On inequalities involving <i>n</i> -polynomial exponential-type convex functions

Abstract This article deals with new generalized and more refined classes of Hermite-Hadamard and Fejér Hermite-Hadamard-type inequalities via <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>n</m:mi> </m:math> n -polynomial exponential-type convex functions. The illustrative graphs confirm the validity of new inequalities. Some applications are provided for generalized means to accommodate different user preferences, device capabilities, and technological advancements. To establish the main results, we primarily use Hölder’s inequality, the power mean inequality, and some other generalized inequalities. These inequalities have strong applicability in the theory of optimization.