The authors establish some new inequalities for differentiable convex functions, which are similar to the celebrated Hermite-Hadamard's integral inequality for convex functions, and apply these inequalities to construct inequalities for special means of two positive numbers.

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Some Integral Inequalities of Hermite-Hadamard Type for Convex Functions with Applications to Means

In this article, we present an identity and several Hermite-Hadamard type inequalities for conformable fractional integrals. As applications, we establish some inequalities for certain special means of two positive real numbers and give the error estimations for the trapezoidal formula.

/pdf/inequalities-for-a-fractional-differentiable-functions-23be05i6px.pdf

Inequalities for α-fractional differentiable functions

The objectives of this paper is to obtain some Hermite-Hadamard type inequalities for h-preinvex functions. Firstly, a new kind of generalized h-convex functions, termed h-preinvex functions, is introduced through relaxing the concept of h-convexity introduced by Varosanec. And the Hermite-Hadamard type inequalities for h-preinvex functions are established under certain conditions. Our results can be viewed as generalization of several previously known results.

/pdf/on-hermite-hadamard-inequalities-for-h-preinvex-functions-57e3iek5f5.pdf

On hermite-hadamard inequalities for h-preinvex functions

In the paper the authors introduce concepts of the m- and (α, m)-geometrically convex functions and establish some inequalities of Hermite–Hadamard type for these classes of functions.

Hermite–Hadamard type inequalities for the m - and ( α , m )-geometrically convex functions

In the paper, the authors, by Holder's inequality, establish some Hermite-Hadamard type integral inequalities for GA-convex functions and apply these inequalities to construct several inequalities for special means.

/pdf/some-inequalities-of-hermite-hadamard-type-for-ga-convex-n57ouae1zi.pdf

Some inequalities of Hermite-Hadamard type for GA-Convex functions with applications to means

In the paper, the authors introduce concepts of m- and (; m)-logarithmically convex functions and establish some Hermite-Hadamard type inequalities of these classes of functions.

/pdf/hermite-hadamard-type-inequalities-for-the-m-and-a-m-4ddo3vd727.pdf

Hermite-Hadamard type inequalities for the m- and (α, m)-logarithmically convex functions

The marginal productivity theory is the modern form of the three-factor theory of value. It is the fundamental theory used in Western economics to describe value creation, as well as the fundamental Western theory dealing with wealth theory in the value category. Its original form is the “trinity formula,” composed of three propositions and formulated more than 200 years ago by Jean-Baptiste Say. Because of internal logical defects in the three propositions, the “trinity formula” is merely a hypothesis, and cannot be accepted as a scientific “theory.” The modern form of the three-factor theory of value is the marginal productivity theory proposed more than 100 years ago by John Bates Clark, and subsequently developed further by other researchers. The marginal productivity theory, however, still suffers from three defects of internal logic, and, correspondingly, from three external theoretical difficulties. The article explains that the marginal productivity theory, the modern form of the factor theory of value, has external deficiencies. First, the subject of distribution cannot be defined; second, the contributions made by the factors cannot be defined; and third, the ownership of the contributions cannot be defined.

/pdf/deficiencies-of-the-three-factor-theory-of-value-3jwx7h3b.pdf

Rui-Fang Bai

Papers

Hermite-Hadamard type inequalities for the m- and (α, m)-logarithmically convex functions

Deficiencies of the Three-Factor Theory of Value