Related papers: Inequalities involving arithmetic functions

In this study, we obtain some new integral inequalities for different classes of convex functions by using some elementary inequalities and classical inequalities like general Cauchy inequality and Minkowski inequality.

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.

This article focuses on the Bohr radius problem for the derivatives of analytic functions, along with a technique of establishing Bohr inequalities in classical and generalized settings.

In this papaer, we put forward some new definitions and integral inequalities by using fairly elementary analysis.

In the present paper we establish some new integral inequalities analogous to the well known Hadamard inequality by using a fairly elementary analysis.

Certain new inequalities for the sums of factorials are presented.

In this paper, we establish some integral ineuqalities for n- times differentiable quasi-convex functions.

The main purpose of the present article is to give some new Hilbert's sum type inequalities, which in special cases yield the classical Hilbert's inequalities. Our results provide some new estimates to these types of inequalities.

Over 300 sequences and many unsolved problems and conjectures related to them are presented herein. These notions, definitions, unsolved problems, questions, theorems corollaries, formulae, conjectures, examples, mathematical criteria, etc.…

We shall give a refinement of the arithmetic-geometric mean inequality.

In this paper, we establish some integral ineuqalities for n- times differentiable convex functions.

This paper deals with generalized elliptic integrals and generalized modular functions. Several new inequalities are given for these and related functions.

The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…

Matrix inequalities that extend certain scalar ones have been at the center of numerous researchers' attention. In this article, we explore the celebrated subadditive inequality for matrices via concave functions and present a reversed…

We will show certain functional inequalities between some products of $x^p - 1$.

This a very brief account of the main line of development of Hardy inequalities.

In this survey, we review the many faces of the Hornich-Hlawka inequality. Several open problems that seem of utmost interest are mentioned.

This article improves the triangle inequality for complex numbers, using the Hermite-Hadamard inequality for convex functions. Then, applications of the obtained refinement are presented to include some operator inequalities. The operator…

This paper aims to characterize the function appearing in the weighted Hermite-Hadamard inequality. We provide improved inequalities for the weighted means as applications of the obtained results. Modifications of the weighted…

We discuss the inequalities for $q$-integrals because of the fact that the inequalities can be very useful in the future mathematical research. Since $q$-integral of a function over an interval $[a,b]$ is defined by the difference of two…