Inequalities for Products of Two Kinds of Convexities and Consequent Results

초록

The product of two convex functions is convex under certain conditions, which have motivated extensions to generalized convexities. In the present paper, we establish new Hermite–Hadamard–type inequalities for the product of m-convex and (α, m)-convex functions. Through the presentation of results for these extended classes, we arrive at inequalities that include classical cases as special cases (e.g., when m = 1 or α = 1). Our results improve and extend already established inequalities to find wider applications in convex analysis and optimization.

키워드