INTEGRAL INEQUALITY REGARDING γ-CONVEX AND γ-CONCAVE FUNCTIONS

The Sugeno fuzzy integral of concave functions

The fuzzy integrals are a kind of fuzzy measures acting on fuzzy sets. They can be viewed as an average membershipvalue of fuzzy sets. The value of the fuzzy integral in a decision making environment where uncertainty is presenthas been well established. Most of the integral inequalities studied in the fuzzy integration context normally considerconditions such as monotonicity or comonotonicity....

Γ-sets and Γ-continuous Functions

JENSEN’S INEQUALITY FOR GG-CONVEX FUNCTIONS

In this paper, we obtain Jensen’s inequality for GG-convex functions. Also, we get in- equalities alike to Hermite-Hadamard inequality for GG-convex functions. Some examples are given.

Outer Γ-convex Functions on a Normed Space

For some given positive γ, a function f is called outer γ-convex if it satisfies the Jensen inequality f(zi) ≤ (1 − λi)f(x0) + λif(x1) for some z0 : = x0, z1, ..., zk : = x1 ∈ [x0, x1] satisfying ‖zi − zi+1‖ ≤ γ, where λi : = ‖x0 − zi‖/‖x0 − x1‖, i = 1, 2, ..., k − 1. Though the Jensen inequality is only required to hold true at some points (although the location of these points is uncertain) o...

Convex and concave relaxations of implicit functions