Related papers: Inequalities involving arithmetic functions
The arithmetic function of two variables is defined. Some properties of the function are given along with the formula that is an analog of the so-called Mobius' inversion formula. A heuristic statement is suggested.
A generalization of Mercer inequality for h-convex function is presented. As application, a weighted generalization of triangle inequality is given.
The main goal of this article is to find the exact difference between a convex function and its secant, as a limit of positive quantities. This idea will be expressed as a convex inequality that leads to refinements and reversals of well…
In this paper, new improvement of celebrated H\"older inequality by means of isotonic linear functionals is established. An important feature of the new inequality obtained in here is that many existing inequalities related to the H\"older…
We give a survey of classical and recent results on sharp constants and symmetry/asymmetry of extremal functions in $1$-dimensional functional inequalities.
Inequalities among symmetric functions are fundamental in various branches of mathematics, thus motivating a systematic study of their structure. Majorization has been shown to characterize inequalities among commonly used symmetric…
In this paper, we obtain some new inequalities for functions whose second derivatives' absolute value is s-convex and log-convex. Also, we give some applications for numerical integration.
Let $K$ be a number field. This paper considers arithmetic functions over $K$, that are, complex valued functions on the set of nonzero integral ideals in $K$. Firstly we generalize some basic results on arithmetic functions. Next we define…
We introduce sequences of functions orthogonal on a finite interval: proper orthogonal rational functions, orthogonal exponential functions, orthogonal logarithmic functions, and transmuted orthogonal polynomials
We begin by shortly recalling a generalized mean value inequality for subharmonic functions, and two applications of it: first a weighted boundary behavior result (with some new references and remarks), and then a borderline case result to…
In this short note, we improve the famous Reid Inequality related to linear operators.
We establish sharp inequalities involving the incomplete Beta and Gamma functions. These inequalities arise in the approximation of generalized Bernstein functions by higher order Thorin-Bernstein functions. Furthermore, new properties of a…
Motivared by Carleman's proof of the isoperimetric inequality in the plane, we study some sharp integral inequalities for harmonic functions on the upper halfspace. We also derive the regularity for nonnegative solutions of the associated…
This thesis determines some of the implications of non-universal and emergent universal statistics on arithmetic correlations and fluctuations of arithmetic functions, in particular correlations amongst prime numbers and the variance of the…
We apply matrix methods to arithmetic functions by associating matrices to the functions in a manner drawn from the theory of symmetric functions. Then we study the characteristic polynomials of the associated matrices.
In this paper, a general integral identity for convex functions is derived. Then, we establish new some inequalities of the Simpson and the Hermite-Hadamard's type for functions whose absolute values of derivatives are convex. Some…
In this paper, we describe s-logarithmically convex functions in the first and second sense which are connected with the ordinary logatihmic convex and s-convex in the first and second sense. Afterwards, some new inequalities related to…
We present a simplified integral of functions of several variables. Although less general than the Riemann integral, most functions of practical interest are still integrable. On the other hand, the basic integral theorems can be obtained…
In this paper, we enumerate enumeration problems and algorithms. This survey is under construction. If you know some results not in this survey or there is anything wrong, please let me know.
The present article is devoted to one example which related to the Salem function. The main attention is given to properties of one type of functions including items related to functional equations, graphs, the Lebesgue integral, etc.