Certain sharp inequalities for differentiable functions and estimation of approximation of functions and their derivatives by cubic interpolation splines

1984 ◽  
Vol 24 (5) ◽  
pp. 723-735 ◽  
Author(s):  
N. P. Korneichuk
Keyword(s):  
Approximation Of Functions ◽  
Differentiable Functions

scholarly journals The best one-sided approximations of the class of differentiable functions by algebraic polynomials in $L_1$ space

2012 ◽  
Vol 20 ◽  
pp. 118
Author(s):  
V.P. Motornyi ◽  
V.V. Sedunova
Keyword(s):  
Algebraic Polynomials ◽  
Approximation Of Functions ◽  
Differentiable Functions

The asymptotic meaning of the best one-sided approximation of functions from the class $W^1_{\infty}$ by algebraic polynomials of degree not greater than $n$ in $L_1$ space is calculated here.

scholarly journals Some estimates of approximation of functions by Hermitian splines

1987 ◽  
pp. 23
Author(s):  
O.V. Davydov
Keyword(s):  
Modulus Of Continuity ◽  
Duality Theorem ◽  
Localization Theorem ◽  
Approximation Of Functions ◽  
Uniform Partition ◽  
Integral Modulus ◽  
Differentiable Functions

We find exact values of approximation by Hermitian splines on the classes of differentiable functions in three new cases, which add to the researches of V.L. Velikin. We obtain the estimate of deviation, which uses the values of integral modulus of continuity. Besides, we generalize the duality theorem of A.A. Ligun and prove the localization theorem that allows to determine the optimality of the uniform partition in the most general case.

Approximation of Functions by Some Types of Szasz-mirakjan Operators

2012 ◽  
Vol 15 (3) ◽  
pp. 173-179
Author(s):  
Sahib Al-Saidy ◽  
◽  
Salim Dawood ◽  
Keyword(s):  
Approximation Of Functions

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 Trigonometric approximation of functions $f(x,y)$ of generalized Lipschitz class by double Hausdorff matrix summability method

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Abhishek Mishra ◽  
Vishnu Narayan Mishra ◽  
M. Mursaleen
Keyword(s):  
Double Fourier Series ◽  
Degree Of Approximation ◽  
Trigonometric Approximation ◽  
Lipschitz Class ◽  
Gamma Delta ◽  
Approximation Of Functions ◽  
Matrix Summability ◽  
Alpha Beta ◽  
Generalized Lipschitz Class ◽  
Hausdorff Matrix

AbstractIn this paper, we establish a new estimate for the degree of approximation of functions $f(x,y)$ f ( x , y ) belonging to the generalized Lipschitz class $Lip ((\xi _{1}, \xi _{2} );r )$ L i p ( ( ξ 1 , ξ 2 ) ; r ) , $r \geq 1$ r ≥ 1 , by double Hausdorff matrix summability means of double Fourier series. We also deduce the degree of approximation of functions from $Lip ((\alpha ,\beta );r )$ L i p ( ( α , β ) ; r ) and $Lip(\alpha ,\beta )$ L i p ( α , β ) in the form of corollary. We establish some auxiliary results on trigonometric approximation for almost Euler means and $(C, \gamma , \delta )$ ( C , γ , δ ) means.

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