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
Author(s):  
P. P. Petrushev ◽  
Vasil Atanasov Popov

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

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

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

2021 ◽  
Vol 76 (2) ◽  
Author(s):  
Leonardo Alese

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.


2020 ◽  
Vol 70 (4) ◽  
pp. 829-838
Author(s):  
Saqib Hussain ◽  
Shahid Khan ◽  
Khalida Inayat Noor ◽  
Mohsan Raza

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.


2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Abhishek Mishra ◽  
Vishnu Narayan Mishra ◽  
M. Mursaleen

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.


2005 ◽  
Vol 12 (4) ◽  
pp. 763-768
Author(s):  
Artur Wachowicz

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.


Sign in / Sign up

Export Citation Format

Share Document