JENSEN’S INEQUALITY FOR GG-CONVEX FUNCTIONS

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.

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 (

New Jensens Type Inequalities for Di¤erentiable Log-convex Functions of Selfadjoint Operators in Hilbert Spaces

Some new Jensen’s type inequalities for di¤erentiable log-convex functions of selfadjoint operators in Hilbert spaces under suitable assumptions for the involved operators are given. Applications for particular cases of interest are also provided. 1. Introduction Jensen’s inequality for convex functions is one of the most important result in the Theory of Inequalities due to the fact that many ...

Refinements to Hadamard’s Inequality for Log-Convex Functions

A Generalised Trapezoid Type Inequality for Convex Functions

X iv :m at h/ 03 05 37 4v 1 [ m at h. N A ] 2 7 M ay 2 00 3 A GENERALISED TRAPEZOID TYPE INEQUALITY FOR CONVEX FUNCTIONS S.S. DRAGOMIR Abstract. A generalised trapezoid inequality for convex functions and applications for quadrature rules are given. A refinement and a counterpart result for the Hermite-Hadamard inequalities are obtained and some inequalities for pdf’s and (HH)−divergence measur...

Stolarsky Type Inequality for Sugeno Integrals on Fuzzy Convex Functions

Recently, Flores-Franulič et al. [A note on fuzzy integral inequality of Stolarsky type, Applied Mathematics and Computation 208 (2008) 55-59] proved the Stolarsky’s inequality for the Sugeno integral on the special class of continuous and strictly monotone functions. This result can be generalized to a general class of fuzzy convex functions in this paper. We also give a fuzzy integral inequal...