On differentiable functions of 𝑛 variables

Differentiable Functions Have Sparse Graphs

Real Analysis Exchange ◽

10.2307/44151153 ◽

1978 ◽

Vol 4 (1) ◽

pp. 91

Author(s):

Laczkovich ◽

Petruska

Keyword(s):

Sparse Graphs ◽

Differentiable Functions

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Some generalizations of the Hermite–Hadamard integral inequality

Journal of Inequalities and Applications ◽

10.1186/s13660-021-02605-y ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Slavko Simić ◽

Bandar Bin-Mohsin

Keyword(s):

Integral Inequality ◽

Target Function ◽

Convexity Property ◽

Concave Functions ◽

Differentiable Functions

AbstractIn this article we give two possible generalizations of the Hermite–Hadamard integral inequality for the class of twice differentiable functions, where the convexity property of the target function is not assumed in advance. They represent a refinement of this inequality in the case of convex/concave functions with numerous applications.

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Explicit, Determinantal, and Recurrent Formulas of Generalized Eulerian Polynomials

Axioms ◽

10.3390/axioms10010037 ◽

2021 ◽

Vol 10 (1) ◽

pp. 37

Author(s):

Yan Wang ◽

Muhammet Cihat Dağli ◽

Xi-Min Liu ◽

Feng Qi

Keyword(s):

General Formula ◽

Bell Polynomials ◽

Eulerian Polynomials ◽

Differentiable Functions ◽

Faà Di Bruno Formula ◽

Derivatives Of

In the paper, by virtue of the Faà di Bruno formula, with the aid of some properties of the Bell polynomials of the second kind, and by means of a general formula for derivatives of the ratio between two differentiable functions, the authors establish explicit, determinantal, and recurrent formulas for generalized Eulerian polynomials.

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A new bound for the Jensen gap pertaining twice differentiable functions with applications

Advances in Difference Equations ◽

10.1186/s13662-020-02794-8 ◽

2020 ◽

Vol 2020 (1) ◽

Cited By ~ 7

Author(s):

Shahid Khan ◽

Muhammad Adil Khan ◽

Saad Ihsan Butt ◽

Yu-Ming Chu

Keyword(s):

Differentiable Functions

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Approximation of Infinitely Differentiable Functions on the Real Line by Polynomials in Weighted Spaces

Journal of Mathematical Sciences ◽

10.1007/s10958-021-05486-0 ◽

2021 ◽

Author(s):

I. Kh. Musin

Keyword(s):

Real Line ◽

Weighted Spaces ◽

The Real ◽

Differentiable Functions ◽

Infinitely Differentiable Functions

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General Norm Inequalities of Trapezoid Type for Fréchet Differentiable Functions in Banach Spaces

Symmetry ◽

10.3390/sym13071288 ◽

2021 ◽

Vol 13 (7) ◽

pp. 1288

Author(s):

Silvestru Sever Dragomir

Keyword(s):

Banach Spaces ◽

Error Bounds ◽

Norm Inequalities ◽

Differentiable Functions ◽

Fréchet Differentiable ◽

General Norm

In this paper we establish some error bounds in approximating the integral by general trapezoid type rules for Fréchet differentiable functions with values in Banach spaces.

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