Generalizations of some remarkable inequalities
Generalizations of the Jensen-Steffensen and related inequalities
We present a couple of general inequalities related to the Jensen-Steffensen inequality in its discrete and integral form. The Jensen-Steffensen inequality, Slater’s inequality and a generalization of the counterpart to the Jensen-Steffensen inequality are deduced as special cases from these general inequalities.
Generalizations of the trapezoid inequalities based on a new mean value theorem for the remainder in Taylor's formula.
Generalizations of weighted version of Ostrowski's inequality and some related results.
Generalized abstracted mean values.
Generalized Bihari type integral inequalities and the corresponding integral equations.
Generalized Hardy operators and normalizing measures.
Generalized matrix versions of the Cauch-Schwarz and Kantorovich inequalities.
Generalized multivariate Jensen-type inequality.
Generalized Ostrowski's inequality on time scales.
Generalized relative information and information inequalities.
Good lower and upper bounds on binomial coefficients.
Gronwall-Bellman-type integral inequalities and applications to BVPs.
Gronwall-OuIang-type integral inequalities on time scales.
Grünbaum-type inequalities for special functions.
Grüss type inequalities for forward difference of vectors in inner product spaces.
Grüss-type bounds for covariances and the notion of quadrant dependence in expectation
We show that Grüss-type probabilistic inequalities for covariances can be considerably sharpened when the underlying random variables are quadrant dependent in expectation (QDE). The herein established covariance bounds not only sharpen the classical Grüss inequality but also improve upon recently derived Grüss-type bounds under the assumption of quadrant dependency (QD), which is stronger than QDE. We illustrate our general results with examples based on specially devised bivariate distributions...