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Inequalities between some arithmetic functions, II [PDF]

Notes on Number Theory and Discrete Mathematics
As a continuation of Part I (see [1]), we offer new inequalities for classical arithmetic functions such as the Euler's totient function, the Dedekind's psi function, the sum of the positive divisors function, the number of divisors function, extended ...
Krassimir Atanassov, József Sándor, Mladen Vassilev-Missana   +2 more
doaj   +2 more sources

Hermite-Hadamard Type Inequalities For Two Times Differentiable Arithmetic-Harmonically Convex Functions

Cumhuriyet Science Journal, 2019
In this work, by using both anintegral identity and the Hölder, the power-mean integral inequalities it isestablished several new inequalities for two times differentiablearithmetic-harmonically-convex function. Also, a few applications are given forsome
Huriye Kadakal
doaj   +4 more sources

Inequalities for the arithmetical functions of Euler and Dedekind [PDF]

Czechoslovak Mathematical Journal, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alzer, Horst, Kwong, Man Kam
openaire   +2 more sources

Jensen Functional, Quasi-Arithmetic Mean and Sharp Converses of Hölder’s Inequalities [PDF]

Mathematics, 2021
In this article, we give sharp two-sided bounds for the generalized Jensen functional Jn(f,g,h;p,x). Assuming convexity/concavity of the generating function h, we give exact bounds for the generalized quasi-arithmetic mean An(h;p,x). In particular, exact bounds are determined for the generalized power means in terms from the class of Stolarsky means ...
Slavko Simić, Vesna Todorčević
openaire   +3 more sources

Essentially large divisors and their arithmetic and function-theoretic inequalities [PDF]

Asian Journal of Mathematics, 2012
Motivated by the classical Theorems of Picard and Siegel and their generalizations, we define the notion of an essentially large effective divisor and derive some of its arithmetic and function-theoretic consequences. We then investigate necessary and sufficient criteria for divisors to be essentially large.
Heier, Gordon, Ru, Min
openaire   +2 more sources

Some inequalities for geometrically-arithmetically h-convex functions [PDF]

Creative Mathematics and Informatics, 2014
In this paper, we consider a class of geometrically convex function which is called geometrically-arithmetically h-convex function. Some inequalities of Hermite-Hadamard type for geometrically-arithmetically h-convex functions are derived. Several special cases are discussed.
MUHAMMAD ASLAM NOOR, KHALIDA INAYAT NOOR, MUHAMMAD UZAIR AWAN   +2 more
openaire   +2 more sources

On certain bounds for the divisor function [PDF]

Notes on Number Theory and Discrete Mathematics
We offer various bounds for the divisor function d(n), in terms of n, or other arithmetical functions.
József Sándor
doaj   +1 more source

Formal Proofs for Nonlinear Optimization [PDF]

, 2015
We present a formally verified global optimization framework. Given a semialgebraic or transcendental function $f$ and a compact semialgebraic domain $K$, we use the nonlinear maxplus template approximation algorithm to provide a certified lower bound of
Allamigeon, Xavier, Gaubert, Stéphane, Magron, Victor, Werner, Benjamin   +3 more
core   +4 more sources

A note on the approximation of divisor functions [PDF]

Notes on Number Theory and Discrete Mathematics
We offer an arithmetic proof of a result from the recent paper [1]. A more general result is provided, too.
József Sándor
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A note on newly introduced arithmetic functions φ+ and σ+ [PDF]

Notes on Number Theory and Discrete Mathematics
In a recent paper [7], the authors introduced new arithmetic functions φ⁺, σ⁺ related to the classical functions φ, and σ, respectively. In this note, we study the behavior of Σ_{n≤x, ω(n)=2}(φ⁺-φ)(n), and Σ_{n≤x, ω(n)=2}(σ⁺-σ)(n), for any real number x ...
Sagar Mandal
doaj   +1 more source