Generalized Newton-like inequalities.
Generalized n-Laplacian: boundedness of weak solutions to the Dirichlet problem with nonlinearity in the critical growth range
Let n ≥ 2 and let Ω ⊂ ℝn be an open set. We prove the boundedness of weak solutions to the problem where ϕ is a Young function such that the space W 01 L Φ(Ω) is embedded into an exponential or multiple exponential Orlicz space, the nonlinearity f(x, t) has the corresponding critical growth, V(x) is a continuous potential, h ∈ L Φ(Ω) is a non-trivial continuous function and µ ≥ 0 is a small parameter. We consider two classical cases: the case of Ω being an open bounded set and the case of Ω =...
Generalized Ostrowski's inequality on time scales.
Generalized relative information and information inequalities.
Generalized -Newton inequalities revisited.
Geometric convexity of a function involving gamma function and applications to inequality theory.
Ger-type and Hyers--Ulam stabilities for the first-order linear differential operators of entire functions.
Global behavior of integral transforms.
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...