scholarly journals Roots of differentiable functions of one real variable

1980 ◽  
Vol 74 (2) ◽  
pp. 441-445 ◽  
Author(s):  
Klaus Reichard
Keyword(s):  
Real Variable ◽  
Differentiable Functions

scholarly journals On the semigroup of differentiable mappings (II)

1972 ◽  
Vol 13 (2) ◽  
pp. 122-128
Author(s):  
G. R. Wood ◽  
Sadayuki Yamamuro
Keyword(s):  
Banach Spaces ◽  
Real Variable ◽  
Differentiable Functions ◽  
Finite Dimensional ◽  
Differentiable Mappings

In [2], K. D. Magill, Jr. has proved that every automorphism of the semigroup (with respect to composition) of all real-valued differentiable functions of a real variable is inner. The purpose of this paper is to generalize this fact to arbitrary finite-dimensional real Banach spaces.

scholarly journals Integral presentation of deviations of rectangular linear means of Fourier series on classes of periodic differentiable functions

2018 ◽  
Vol 32 ◽  
pp. 92-103
Author(s):  
Oleg Novikov ◽  
Olga Rovenska
Keyword(s):  
Fourier Series ◽  
Real Variable ◽  
Upper Bounds ◽  
Integral Representations ◽  
Linear Operators ◽  
Trigonometric Polynomials ◽  
Periodic Functions ◽  
Differentiable Functions ◽  
Fourier Sums ◽  
Linear Means

The paper deals with the problems of approximation in a uniform metric of periodic functions of many variables by trigonometric polynomials, which are generated by linear methods of summation of Fourier series. Questions of asymptotic behavior of the upper bounds of deviations of linear operators generated by the use of linear methods of summation of Fourier series on the classes of periodic differentiable functions are studied in many works. Methods of investigation of integral representations of deviations of polynomials on the classes of periodic differentiable functions of real variable originated and received its development through the works of S.M. Nikol'skii, S.B. Stechkin, N.P.Korneichuk, V.K. Dzadik, A.I. Stepanets, etc. Along with the study of approximation by linear methods of classes of functions of one variable, are studied similar problems of approximation by linear methods of classes of functions of many variables. In addition to the approximative properties of rectangular Fourier sums, are studied approximative properties of other approximation methods: the rectangular sums of Valle Poussin, Zigmund, Rogozinsky, Favar. In this paper we consider the classes of \(\overline{\psi}\)-differentiable periodic functions of many variables, allowing separately to take into account the properties of partial and mixed \(\overline{\psi}\)-derivatives, and given by analogy with the classes of \(\overline{\psi}\)-differentiable periodic functions of one variable. Integral representations of rectangular linear means of Fourier series on classes of \(\overline{\psi}\)-differentiable periodic functions of many variables are obtained. The obtained formulas can be useful for further investigation of the approximative properties of various linear rectangular methods on the classes \(\overline{\psi}\)-differentiable periodic functions of many variables in order to obtain a solution to the corresponding Kolmogorov-Nikolsky problems.

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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