We establish a refinement of the discrete Chebyshev inequality and an analogous one for the Popoviciu inequality.

We give a short and elementary proof of an inverse Bernsteintype inequality found by S. Khrushchev for the derivative of a polynomial having all its zeros on the unit circle . The inequality is used to show that equally-spaced points solve a min-max-min problem for the logarithmic potential of such polynomials. Using techniques recently developed for polarization (Chebyshev-type) problems, we s...

we derive whole series of new integral inequalities of the hardy-type, with non-conjugate exponents. first, we prove and discuss two equivalent general inequa-li-ties of such type, as well as their corresponding reverse inequalities. general results are then applied to special hardy-type kernel and power weights. also, some estimates of weight functions and constant factors are obtained. ...

In the present paper we prove the Chebyshev inequality involving two isotonic linear functionals. Namely, if A and B are isotonic linear functionals, then A(p f g)B(q)+A(p)B(q f g) A(p f )B(qg) + A(pg)B(q f ) , where p,q are non-negative weights and f ,g are similarly ordered functions such that the above-mentioned terms are well-defined. If functionals are equal, i.e. A = B and if p = q , then...

In this paper, some results of the Chebyshev type integral inequality for the pseudo-integral are proven. The obtained results, are related to the measure of a level set of the maximum and the sum of two non-negative integrable functions. Finally, we applied our results to the case of comonotone functions.

In this article, we derive a new generalization of Chebyshev inequality for random vectors. We demonstrate that the new generalization is much less conservative than the classical generalization. 1 Classical Generalization of Chebyshev inequality The Chebyshev inequality discloses the fundamental relationship between the mean and variance of a random variable. Extensive research works have been...

Interpolation was a topic in which Sharma was viewed as an almost uncontested world expert by his collaborators and many other colleagues. We survey recent results for exponential sums and linear combinations of shifted Gaussians which were obtained via interpolation. To illustrate the method exploiting the Pinkus-Smith Improvement Theorem for spans of Descartes systems, we present the proof of...

Article history: Received 1 January 2012 Received in revised form 10 July 2012 Accepted 18 February 2013 Available online 26 February 2013

Integral inequalities are very important in applied sciences. Chebyshev's integral inequality is widely used mathematics. First of all, some necessary definitions and results regarding conformable derivative given this article. Then we give Chebyshev for simultaneously positive (or negative) functions using the fractional derivative. We Gronwall to prove our results, unlike other studies litera...