scholarly journals Uniqueness of best approximation of a function and its derivatives

1973 ◽  
Vol 7 (3) ◽  
pp. 213-225 ◽  
Author(s):  
Bruce L Chalmers
Keyword(s):  
Best Approximation ◽  
Approximation Of A Function ◽  
Uniqueness Of Best Approximation

scholarly journals Approximation of Functions in Besov Space

2021 ◽  
Vol 52 ◽  
Author(s):  
Hare Krishna Nigam ◽  
Supriya Rani
Keyword(s):  
Fourier Series ◽  
Besov Space ◽  
Best Approximation ◽  
Approximation Of Functions ◽  
Approximation Of A Function

In the present paper, we establish a theorem on best approximation of a function g ∈ Bqλ(Lr) of its Fourier series. Our main theorem generalizes some known results of this direction of work. Thus, the results of [10], [26] and [27] become the particular case of our main Theorem 3.1.

scholarly journals Proximinality and co-proximinality in metric linear spaces

2015 ◽  
Vol 69 (1) ◽  
pp. 83
Author(s):  
T. W. Narang ◽  
Sahil Gupta
Keyword(s):  
Best Approximation ◽  
Existence And Uniqueness ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Best Coapproximation ◽  
Uniqueness Of Best Approximation

As a counterpart to best approximation, the concept of best coapproximation was introduced in normed linear spaces by C. Franchetti and M. Furi in 1972. Subsequently, this study was taken up by many researchers. In this paper, we discuss some results on the existence and uniqueness of best approximation and best coapproximation when the underlying spaces are metric linear spaces.

scholarly journals Proximinality and co-proximinality in metric linear spaces

2015 ◽  
Vol 69 (1) ◽  
Author(s):  
T.D. Narang ◽  
Sahil Gupta
Keyword(s):  
Best Approximation ◽  
Existence And Uniqueness ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Best Coapproximation ◽  
Uniqueness Of Best Approximation

AbstractAs a counterpart to best approximation, the concept of best coapproximation was introduced in normed linear spaces by C. Franchetti and M. Furi in 1972. Subsequently, this study was taken up by many researchers. In this paper, we discuss some results on the existence and uniqueness of best approximation and best coapproximation when the underlying spaces are metric linear spaces

scholarly journals Approximation of a Function in Hölder Class Using Double Karamata (Kλ,μ) Method

2020 ◽  
Vol 13 (3) ◽  
pp. 567-578
Author(s):  
H. K. Nigam ◽  
Md. Hadish
Keyword(s):  
Fourier Series ◽  
Best Approximation ◽  
Double Fourier Series ◽  
Hölder Class ◽  
The Best Approximation ◽  
Holder Class ◽  
Function Of Two Variables ◽  
Approximation Of A Function

In this paper, we establish a new theorem on the best approximation of a function of two variables belonging to H ̈older class by double Karamata (Kλ,μ) means of its double Fourier series.

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