ON QUASI CONVEX FUNCTIONS AND HADAMARD'S INEQUALITY

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.

An inequality related to $eta$-convex functions (II)

Using the notion of eta-convex functions as generalization of convex functions, we estimate the difference between the middle and right terms in Hermite-Hadamard-Fejer inequality for differentiable mappings. Also as an application we give an error estimate for midpoint formula.

Quasi-convex Functions and Quasi-monotone Operators

The notions of a quasi-monotone operator and of a cyclically quasi-monotone operator are introduced, and relations between such operators and quasi-convex functions are established.

Some Properties of Certain Subclasses of Close-to-Convex and Quasi-convex Functions with Respect to 2k-Symmetric Conjugate Points

Jensen’s Operator Inequality for Strongly Convex Functions

We give a Jensen’s operator inequality for strongly convex functions. As a corollary, we improve Hölder-McCarthy inequality under suitable conditions. More precisely we show that if Sp (A) ⊂ I ⊆ (1,∞), then 〈Ax, x〉 r ≤ 〈Ax, x〉 − r − r 2 (