Related papers: An inequality for correlated measurable functions

An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.

In this paper, we present some double inequalities involving certain ratios of the Gamma function. These results are further generalizations of several previous results. The approach is based on the monotonicity properties of some functions…

Similarity metric which is not positive definite, and present a general theorem which provides a large family of similarity metrics which are positive definite.

We study arithmetic inequalities for multiplicative, sub(super)-multiplicative, sub(super)-homogeneous functions. Applications for the classical arithmetic functions are pointed out.

In this paper, we prove Newton-Maclaurin type inequalities for functions obtained by linear combination of two neighboring primary symmetry functions, which is a generalization of the classical Newton-Maclaurin inequality.

In this paper, we establish Newton-Maclaurin type inequalities for functions arising from linear combinations of primitively symmetric polynomials. This generalization extends the classical Newton-Maclaurin inequality to a broader class of…

A common statistical task lies in showing asymptotic normality of certain statistics. In many of these situations, classical textbook results on weak convergence theory suffice for the problem at hand. However, there are quite some…

In this paper, we investigate the complete monotonicity of some functions involving gamma function. Using the monotonic properties of these functions, we derived some inequalities involving gamma and beta functions. Such inequalities…

The classical theory of symmetric functions has a central position in algebraic combinatorics, bridging aspects of representation theory, combinatorics, and enumerative geometry. More recently, this theory has been fruitfully extended to…

We generalize the classical probability frame by adopting a wider family of random variables that includes nondeterministic ones. The frame that emerges is known to host a ''classical'' extension of quantum mechanics. We discuss the notion…

These are classified by the direction of approximation (from above or below), the set family types (partition or covering) of simple functions, the coefficient signature (non-negative or signed), and cardinal number of terms of simple…

We derive families of Newton-like inequalities involving the elementary symmetric functions of sets of self-conjugate complex numbers in the right half-plane. These are the first known inequalities of this type which are independent of the…

In this article, we prove a normality criterion for a family of meromorphic functions having zeros with some multiplicity which involves sharing of a holomorphic function by the members of the family. Our result generalizes Montel's…

In general, some of the well known results of measure theory dealing with the convergence of sequences of functions such as the Dominated Convergence Theorem or the Monotone Convergence Theorem are not true when we consider arbitrary nets…

By making use of the familiar Mathieu series and its generalizations, the authors derive a number of new integral representations and present a systematic study of probability density functions and probability distributions associated with…

We prove two conjectures on correlation inequalities for functions that are linear combinations of unimodal Boolean monotone nondecreasing functions

In the paper, we establish an inequality involving the gamma and digamma functions and use it to prove the negativity and monotonicity of a function involving the gamma and digamma functions.

A class of functions involving the divided differences of the psi function and the polygamma functions and originating from Kershaw's double inequality are proved to be completely monotonic. As applications of these results, the…

We define two-parameter families of noncommutative symmetric functions and quasi-symmetric functions, which appear to be the proper analogues of the Macdonald symmetric functions in these settings.

We utilize operational methods to generalize the Chernoff inequality and prove a new result that relates the moment bound to strictly absolute monotonic functions. We show that the Chernoff bound is part of a continuum of probability…