Normed algebras of differentiable functions on compact plane sets: completeness and semisimple completions

2011 ◽  
Vol 207 (1) ◽  
pp. 19-45 ◽  
Author(s):  
Heiko Hoffmann
Keyword(s):  
Differentiable Functions ◽  
Compact Plane

scholarly journals PROPERTIES OF CERTAIN SUBALGEBRAS OF DALES-DAVIE ALGEBRAS

2007 ◽  
Vol 49 (2) ◽  
pp. 225-233 ◽  
Author(s):  
M. ABTAHI ◽  
T. G. HONARY
Keyword(s):  
Maximal Ideal ◽  
Rational Functions ◽  
Maximal Ideal Space ◽  
Analytic Extension ◽  
Ideal Space ◽  
Differentiable Functions ◽  
Function Algebras ◽  
Infinitely Differentiable Functions ◽  
Interesting Class ◽  
Compact Plane

AbstractWe study an interesting class of Banach function algebras of infinitely differentiable functions on perfect, compact plane sets. These algebras were introduced by H. G. Dales and A. M. Davie in 1973, called Dales-Davie algebras and denoted by D(X, M), where X is a perfect, compact plane set and M = {Mn}∞n = 0 is a sequence of positive numbers such that M0 = 1 and (m + n)!/Mm+n ≤ (m!/Mm)(n!/Mn) for m, n ∈ N. Let d = lim sup(n!/Mn)1/n and Xd = {z ∈ C : dist(z, X) ≤ d}. We show that, under certain conditions on X, every f ∈ D(X, M) has an analytic extension to Xd. Let DP [DR]) be the subalgebra of all f ∈ D(X, M) that can be approximated by the restriction to X of polynomials [rational functions with poles off X]. We show that the maximal ideal space of DP is $X^_d$, the polynomial convex hull of Xd, and the maximal ideal space of DR is Xd. Using some formulae from combinatorial analysis, we find the maximal ideal space of certain subalgebras of Dales-Davie algebras.

Differentiable Functions Have Sparse Graphs

1978 ◽  
Vol 4 (1) ◽  
pp. 91
Author(s):  
Laczkovich ◽  
Petruska
Keyword(s):  
Sparse Graphs ◽  
Differentiable Functions

scholarly journals Some generalizations of the Hermite–Hadamard integral inequality

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.

scholarly journals Explicit, Determinantal, and Recurrent Formulas of Generalized Eulerian Polynomials

Axioms ◽  
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.

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

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shahid Khan ◽  
Muhammad Adil Khan ◽  
Saad Ihsan Butt ◽  
Yu-Ming Chu
Keyword(s):  
Differentiable Functions

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

Symmetry ◽  
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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