New Hadamard Type Inequalities for Modified h-Convex Functions

Abstract

In this article, we demonstrated various Hermite–Hadamard and Fejér type inequalities for modified h-convex functions. We showed several inequalities for the products of two modified h-convex functions. New identities related to inequalities in various forms are also established for different values of the h(φt) function. We believe that the approach presented in this paper will inspire more research in this area.

On Hermite–Hadamard-Type Inequalities for Functions Satisfying Second-Order Differential Inequalities

“…Some improvements and extensions of the above result have been obtained by some authors, see, e.g., [4][5][6][7]. Other extensions of (1) to various classes of functions have been obtained: s-convex functions [8][9][10][11], log-convex functions [12][13][14], h-convex functions [15,16], and m-convex functions [17][18][19][20]. For other classes of functions, we refer to [21][22][23][24] and the references therein.…”

Some Further Results Using Green’s Function for s -Convexity

“…Lemma 6. Let ϖ < ϕ and ℘: [ϖ, ϕ] ⟶ R be a twice differentiable function and G κ (κ � 1, 2, 3, 4) be the new Green's functions defned by (12). Ten,…”

“…On the other hand, there are a lot of new issues in applied mathematics where the idea of convexity is insufcient to adequately characterize them in order to have benefcial consequences. Because of this, the idea of convexity has been expanded upon and developed in various research studies; see [10][11][12][13][14][15][16].…”

Fractional Hermite–Hadamard-Type Inequalities for Differentiable Preinvex Mappings and Applications to Modified Bessel and q-Digamma Functions

“…Convexity is well known as playing a significant and critical role in a range of domains such as economics, finance, optimization, game theory, statistical theory, quality management, and numerous sciences. For the literature regarding convexity, see the references [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”