Results 31 to 40 of about 53,918 (234)

Some new arithmetic functions [PDF]

Notes on Number Theory and Discrete Mathematics
We introduce and study some new arithmetic functions, connected with the classical functions φ (Euler's totient), ψ (Dedekind's function) and σ (sum of divisors function).
József Sándor, Krassimir Atanassov
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

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

On HT-convexity and Hadamard-type inequalities

Journal of Inequalities and Applications, 2020
In the paper, the authors define a new notion of “HT-convex function”, present some Hadamard-type inequalities for the new class of HT-convex functions and for the product of any two HT-convex functions, and derive some inequalities for the arithmetic ...
Shu-Ping Bai, Shu-Hong Wang, Feng Qi
doaj   +1 more source

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
doaj   +1 more source

On Fejér’s inequality: generalizations and applications

Journal of Inequalities and Applications, 2023
This paper deals with generalizations and refinements of Fejér’s inequality with some new applications. We introduce a real mapping M f ω ( t ) $\mathcal{M}_{f}^{\omega}(t)$ and obtain some its functional properties.
Mohsen Rostamian Delavar
doaj   +1 more source

Refinements of bounds for the arithmetic mean by new Seiffert-like means

AIMS Mathematics, 2021
In the article, we present the sharp upper and lower bounds for the arithmetic mean in terms of new Seiffert-like means, which give some refinements of the results obtained in [1].
Wei-Mao Qian, Tie-Hong Zhao, Yu-Pei Lv
doaj   +1 more source

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

Some sharp inequalities involving Seiffert and other means and their concise proofs [PDF]

, 2012
In the paper, by establishing the monotonicity of some functions involving the sine and cosine functions, the authors provide concise proofs of some known inequalities and find some new sharp inequalities involving the Seiffert, contra-harmonic ...
Jiang, Wei-Dong, Qi, Feng
core   +1 more source

Corrected Dual-Simpson-Type Inequalities for Differentiable Generalized Convex Functions on Fractal Set

Fractal and Fractional, 2022
The present paper provides several corrected dual-Simpson-type inequalities for functions whose local fractional derivatives are generalized convex. To that end, we derive a new local fractional integral identity as an auxiliary result.
Abdelghani Lakhdari, Wedad Saleh, Badreddine Meftah, Akhlad Iqbal   +3 more
doaj   +1 more source