Results 11 to 20 of about 1,052 (202)

Some new fractional Hermite-Hadamard type inequalities for functions with co-ordinated extended s,m-prequasiinvex mixed partial derivatives

Alexandria Engineering Journal, 2023
This article introduces extended (s,m)-prequasiinvex functions on coordinates, a new form of generalized convex function. Using a previously established identity, we derive new fractional Hermite-Hadamard type integral inequalities for functions whose ...
Wedad Saleh, Abdelghani Lakhdari, Adem Kiliçman, Assia Frioui, Badreddine Meftah   +4 more
doaj   +1 more source

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 arithmetical products involving the divisors of an integer [PDF]

Notes on Number Theory and Discrete Mathematics
We study the arithmetical products Π d^d, Πd^{1/d} and Πd^{log d}, where d runs through the divisors of an integer n>1.
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

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

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

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

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

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