Related papers: Inequalities involving arithmetic functions
The main goal of this work is to present new matrix inequalities of the Cauchy-Schwarz type. In particular, we investigate the so-called Lieb functions, whose definition came as an umbrella of Cauchy-Schwarz-like inequalities, then we…
In this note, we present a refinement of the well-known AM-GM inequality. We use this improved inequalty to establish corresponding inequalities on Hilbert space. We also give some refinements of the Kantorovich inequality.
The purpose of this paper is to provide a random version of Simons' inequality.
In this article, we prove that convex functions and log-convex functions obey certain general refinements that lead to several refinements and reverses of well known inequalities for matrices, including Young's inequality, Heinz inequality,…
In this note we consider inequalities involving the error function $\phi$. Our methodes give new proofs of some known inequalities of Komatsu, and of Szarek and Werner, and also produce two families of inequalities that give upper and lower…
For a real-valued non-negative and log-concave function we introduce a notion of difference function; the difference function represents a functional analog on the difference body of a convex body. We prove a sharp inequality which bounds…
In this paper, we define \varphi_{h,m}-convex functions and prove some inequalities for this class.
We investigate uniqueness problems for an entire function that shares two small functions of finite order with their difference operators. In particular, we give a generalization of a result in $[2]$.
We discuss some different results on Sidon-type inequalities and on the space of quasi-continuous functions.
In this paper we give simple proofs for the bounds (some of them sharp) of the difference of the moduli of the second and the first logarithmic coefficient for the general class of univalent functions and for the class of convex univalent…
Considering some parameters and by means of an inequality of Hadamard, we derive general half-discrete Hilbert-type inequalities. Then we highlight some special cases.
The aim of this paper is to present some new Fejer-type results for convex functions. Improvements of Young's inequality (the arithmetic-geometric mean inequality) and other applications to special means are pointed as well.
The estimate in Bullen's inequality will be extended for continuous functions using the second order modulus of smoothness. A different form of this inequality will be given in terms of the least concave majorant. Also, the composite case…
Some properties of integral averages of functions on intervals and their asymptotic behavior are investigated. The results are aimed at applications to entire and subharmonic functions.
The Additive Transform of an arithmetic function represents a novel approach to examining the interplay between multiplicative arithmetic function and additive functions. This transform concept introduces a method to systematically generate…
Several inequalities for eigenvalues involving convex combinations and compressions are given. These inequalities are matrix version of the basic convexity inequality f((a+b)/2) < (f(a)+f(b))/2.
Various miscellaneous functional inequalities are deduced for the so-called generalized inverse trigonometric and hyperbolic functions. For instance, functional inequalities for sums, difference and quotient of generalized inverse…
We study the symmetry in short intervals of arithmetic functions with non-negative exponential sums.
In this work, a generalization of the well known Bernoulli inequality is obtained by using the theory of discrete fractional calculus. As far as we know our approach is novel.
In this letter, we prove an inequality involving alternating binomial logarithmic sums by exploiting the variance of the logarithm of the maximum of independent and identically distributed exponential random variables. This inequality was…