Related papers: Inequalities for multiplicative arithmetic functio…
In this paper, we prove some new inequalities of Hadamard-type for convex functions on the co-ordinates.
In this paper, we present some new inequalities for the gamma function. The main tools are the multiple-correction method developed in our previous works, and a generalized Mortici's lemma.
The classical quadratic formula and some of its lesser known variants for solving the quadratic equation are reviewed. Then, a new formula for the roots of a quadratic polynomial is presented.
In the paper, some lower bounds for polygamma functions are refined.
In this paper, we establish some new Hadamard type inequalities using elementary well known inequalities for functions whose inequalities absolute values are {\alpha}-, m-, ({\alpha},m)-logarithmically convex.
We study the symmetry in short intervals of arithmetic functions with non-negative exponential sums.
We give a survey of classical and recent results on sharp constants and symmetry/asymmetry of extremal functions in $1$-dimensional functional inequalities.
An unconditional inequality of the totient function is contributed to the literature. This result is associated with various problems about the distribution of prime numbers.
Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…
In this paper we give effective estimates for some classical arithmetic functions defined over prime numbers. First we find the smallest real number $x_0$ so that some inequality involving Chebyshev's $\vartheta$-function holds for every $x…
In this paper, we establish three inequalities for differentiable s-geometrically and geometrically convex functions which are connected with the famous Hermite-Hadamard inequality holding for convex functions. Some applications to special…
Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…
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…
We present a treasure trove of open problems in matrix and operator inequalities, of a functional analytic nature, and with various degrees of hardness.
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…
Based on collection of bijections, variable and function are extended into ``isomorphic variable'' and ``dual-variable-isomorphic function'', then mean values such as arithmetic mean and mean of a function are extended to ``isomorphic…
In this paper, we establish some new Ostrowski type inequalities for the class of h-convex functions which are super-multiplicative or super-additive and nonnegative. Some applications for special means and PDF's are given.
In this paper, we introduce the concept of operator arithmetic-geometrically convex functions for positive linear operators and prove some Hermite-Hadamard type inequalities for these functions. As applications, we obtain trace inequalities…
Simple inequalities for some integrals involving the modified Struve function of the first kind $\mathbf{L}_{\nu}(x)$ are established. In most cases, these inequalities have best possible constant. We also deduce a tight double inequality,…
We study the arithmetic property which allows to sharpen number-theoretic estimates. Previous results on this property are, as a rule, quantitive. The application of our general qualitive theorems to generalized hypergeometric functions…