Related papers: On the Jensen functional and superterzaticity

We study the Mercer inequality and its operator extension for superquadratic functions. In particular, we give a more general form of the Mercer inequality by replacing some constants by positive operators. As some consequences, our results…

In this paper we obtain new canonical synergetic formula, namely an $\zeta$-analogue of next elementary trigonometric formula. This one describes cooperative interactions between corresponding class of elementary functions and the Riemann's…

A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables…

In the paper we prove a new upper bound for Heilbronn's exponential sum and obtain some applications of our result to distribution of Fermat quotients.

Abstrct: In this note, by considering fractionally linear functions over a finite field and consequently developing an abstract sequence, we study some of its properties.

This paper provides some expansions of Riemann xi function, $\xi$, as a series of Bessel K functions.

In this work, the notions of normal cones at infinity to unbounded sets and limiting and singular subdifferentials at infinity for extended real value functions are introduced. Various calculus rules for these notions objects are…

Several sets of quaternionic functions are described and studied. Residue current of the right inverse of a quaternionic function is introduced in particular cases.

More precise estimates for the Bergman metric on strongly pseudoconvex domains are given, based on the use of the squeezing function.

We offer some partition functions related to ternary quadratic forms, and note on their upper bounds and related properties. We offer these results as an application of a simple method related to conjugate Bailey pairs presented in a prior…

We give new lower bounds for $L^p$ estimates of the Schr\"odinger maximal function by generalizing an example of Bourgain.

We provide explicit bounds in the theory of the Riemann zeta-function at the line $\Re{s}=1$, assuming that the Riemann hypothesis holds until the height $T$. In particular, we improve some bounds, in finite regions, for the logarithmic…

In this article, we define a very important sequence of functions, all the functions of this sequence present behaviors very close to that of the Collatz function. The study of such functions allows us to obtain very interesting results…

The Central Limit Theorem for Iterated Functions Systems on the circle is proved. We study also ergodicity of such systems.

In this paper we establish the Ulam stability of Jensen functional inequality in some classes of groups.

We prove lower bounds for the Hausdorff measure of nodal sets of eigenfunctions.

In the setup of i.i.d.~observations and a real valued differentiable functional~$T$, locally asymptotic upper bounds are derived for the power of one-sided tests (simple, versus large values of~$T$)and for the confidence probability of…

In this paper we give a new integral expression of I and J-Bessel functions on simple Euclidean Jordan algebras, integrating on a bounded symmetric domain. From this we easily get the upper estimate of Bessel functions. As an application we…

We present some new lower bound estimates for certain numbers in Laver table theory and introduce several related structures of interest.

We re-examine perturbative and nonperturbative aspects of the beta function in N=1 and N=2 supersymmetric gauge theories, make comments on the recent literature on the subject and discuss the exactness of several known results such as the…