Degree of Approximation of Real Functions by Reciprocals of Real and Complex Polynomials

1988 ◽  
Vol 19 (1) ◽  
pp. 233-245 ◽  
Author(s):  
A. L. Levin ◽  
E. B. Saff
Keyword(s):  
Degree Of Approximation ◽  
Complex Polynomials ◽  
Real Functions

Rational Approximation of Real Functions

1988 ◽  
Author(s):  
P. P. Petrushev ◽  
Vasil Atanasov Popov
Keyword(s):  
Rational Approximation ◽  
Real Functions

Differentiable Restrictions of Real Functions

1987 ◽  
Vol 13 (1) ◽  
pp. 40
Author(s):  
Brown
Keyword(s):  
Real Functions

ON THE MEASURABLE BOUNDARIES OF REAL FUNCTIONS

1995 ◽  
Vol 21 (1) ◽  
pp. 83
Author(s):  
Wagner-Bojakowska
Keyword(s):  
Real Functions

ω₁-LIMITS OF REAL FUNCTIONS

1999 ◽  
Vol 25 (1) ◽  
pp. 89 ◽  
Author(s):  
Natkaniec
Keyword(s):  
Real Functions

scholarly journals Affine Subspaces of Curvature Functions from Closed Planar Curves

2021 ◽  
Vol 76 (2) ◽  
Author(s):  
Leonardo Alese
Keyword(s):  
Arc Length ◽  
Planar Curves ◽  
Affine Subspaces ◽  
Planar Curve ◽  
Real Functions ◽  
Discrete Counterpart ◽  
Equivalent Conditions

AbstractGiven a pair of real functions (k, f), we study the conditions they must satisfy for $$k+\lambda f$$ k + λ f to be the curvature in the arc-length of a closed planar curve for all real $$\lambda $$ λ . Several equivalent conditions are pointed out, certain periodic behaviours are shown as essential and a family of such pairs is explicitely constructed. The discrete counterpart of the problem is also studied.

Coefficient inequalities related with typically real functions

2020 ◽  
Vol 70 (4) ◽  
pp. 829-838
Author(s):  
Saqib Hussain ◽  
Shahid Khan ◽  
Khalida Inayat Noor ◽  
Mohsan Raza
Keyword(s):  
Unit Disk ◽  
Real Functions ◽  
Coefficient Inequalities ◽  
Typically Real ◽  
Class Of Functions ◽  
Typically Real Functions

AbstractIn this paper, we are mainly interested to study the generalization of typically real functions in the unit disk. We study some coefficient inequalities concerning this class of functions. In particular, we find the Zalcman conjecture for generalized typically real 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.

scholarly journals Preimages of Residual Sets of Continuous Functions under Operation of Superposition

2005 ◽  
Vol 12 (4) ◽  
pp. 763-768
Author(s):  
Artur Wachowicz
Keyword(s):  
Banach Space ◽  
Continuous Functions ◽  
Real Functions ◽  
Second Category ◽  
Residual Sets

Abstract Let 𝐶 = 𝐶[0, 1] denote the Banach space of continuous real functions on [0, 1] with the sup norm and let 𝐶* denote the topological subspace of 𝐶 consisting of functions with values in [0, 1]. We investigate the preimages of residual sets in 𝐶 under the operation of superposition Φ : 𝐶 × 𝐶* → 𝐶, Φ(𝑓, 𝑔) = 𝑓 ○ 𝑔. Their behaviour can be different. We show examples when the preimages of residual sets are nonresidual of second category, or even nowhere dense, and examples when the preimages of nontrivial residual sets are residual.

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