Best uniform approximation in the metric space of continuous mappings with compact convex images

2011 ◽  
Vol 62 (12) ◽  
pp. 1879-1895
Author(s):  
Yu. V. Hnatyuk
Keyword(s):  
Metric Space ◽  
Uniform Approximation ◽  
Compact Convex ◽  
Best Uniform Approximation ◽  
Continuous Mappings

scholarly journals Solution of Fractional Differential Equations Utilizing Symmetric Contraction

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Aftab Hussain
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fractional Differential Equations ◽  
Metric Space ◽  
Metric Spaces ◽  
Order Differential Equation ◽  
Fractional Order Differential Equation ◽  
Continuous Mappings ◽  
Fractional Differential ◽  
Fixed Point Technique

The aim of this paper is to present another family of fractional symmetric α - η -contractions and build up some new results for such contraction in the context of ℱ -metric space. The author derives some results for Suzuki-type contractions and orbitally T -complete and orbitally continuous mappings in ℱ -metric spaces. The inspiration of this paper is to observe the solution of fractional-order differential equation with one of the boundary conditions using fixed-point technique in ℱ -metric space.

Continuous mappings in grey metric space

2022 ◽  
Author(s):  
G. Rohini Vijaya Laxmi ◽  
J. Subhashini
Keyword(s):  
Metric Space ◽  
Continuous Mappings

Čebyšev Sets in Hyperspaces over Rn

2009 ◽  
Vol 61 (2) ◽  
pp. 299-314 ◽  
Author(s):  
Robert J. MacG. Dawson and ◽  
Maria Moszyńska
Keyword(s):  
Metric Space ◽  
Convex Sets ◽  
Compact Convex ◽  
Hausdorff Metric ◽  
Linear Structure ◽  
Convex Compact ◽  
Nearest Neighbour ◽  
Compact Sets ◽  
Strictly Convex ◽  
Convex Compact Sets

Abstract. A set in a metric space is called a Čebyšev set if it has a unique “nearest neighbour” to each point of the space. In this paper we generalize this notion, defining a set to be Čebyšev relative to another set if every point in the second set has a unique “nearest neighbour” in the first. We are interested in Čebyšev sets in some hyperspaces over Rn, endowed with the Hausdorff metric, mainly the hyperspaces of compact sets, compact convex sets, and strictly convex compact sets. We present some new classes of Čebyšev and relatively Čebyšev sets in various hyperspaces. In particular, we show that certain nested families of sets are Čebyšev. As these families are characterized purely in terms of containment,without reference to the semi-linear structure of the underlyingmetric space, their properties differ markedly from those of known Čebyšev sets.

Note on Best Approximation of |x|

1979 ◽  
Vol 22 (3) ◽  
pp. 363-366
Author(s):  
Colin Bennett ◽  
Karl Rudnick ◽  
Jeffrey D. Vaaler
Keyword(s):  
General Problem ◽  
Uniform Approximation ◽  
Best Approximation ◽  
Best Uniform Approximation ◽  
Linear Fractional Transformations ◽  
Symmetric Complex ◽  
Image Position ◽  
Complex Valued ◽  
Special Case

In this note the best uniform approximation on [—1,1] to the function |x| by symmetric complex valued linear fractional transformations is determined. This is a special case of the more general problem studied in [1]. Namely, for any even, real valued function f(x) on [-1,1] satsifying 0 = f ( 0 ) ≤ f (x) ≤ f (1) = 1, determine the degree of symmetric approximationand the extremal transformations U whenever they exist.

The best uniform approximation of ellipse with degree two

2017 ◽  
Author(s):  
Abedallah Rababah ◽  
Zainab AlMeraj
Keyword(s):  
Uniform Approximation ◽  
Best Uniform Approximation

scholarly journals Concentration of the error between a function and its polynomial of best uniform approximation

1998 ◽  
Vol 41 (3) ◽  
pp. 447-463 ◽  
Author(s):  
Maurice Hasson
Keyword(s):  
Uniform Approximation ◽  
Algebraic Polynomial ◽  
General Class ◽  
Supremum Norm ◽  
Best Uniform Approximation ◽  
Class A ◽  
Image Position ◽  
Class Of Functions

Let f be a continuous real valued function defined on [−1, 1] and let En(f) denote the degree of best uniform approximation to f by algebraic polynomial of degree at most n. The supremum norm on [a, b] is denoted by ∥.∥[a, b] and the polynomial of degree n of best uniform approximation is denoted by Pn. We find a class of functions f such that there exists a fixed a ∈(−1, 1) with the following propertyfor some positive constants C and N independent of n. Moreover the sequence is optimal in the sense that if is replaced by then the above inequality need not hold no matter how small C > 0 is chosen.We also find another, more general class a functions f for whichinfinitely often.

A Haar-type theory of best uniform approximation with constraints

1991 ◽  
Vol 58 (3-4) ◽  
pp. 351-374 ◽  
Author(s):  
A. Kroó ◽  
D. Schmidt
Keyword(s):  
Uniform Approximation ◽  
Type Theory ◽  
Best Uniform Approximation
Sign in / Sign up

Export Citation Format

Share Document