Representation of continuous functions of three variables by the superposition of continuous functions of two variables

1963 ◽  
pp. 61-147 ◽  
Author(s):  
V. I. Arnol′d
Keyword(s):  
Continuous Functions ◽  
Functions Of Two Variables

Smooth approximations by continuous choice-functions

2021 ◽  
Author(s):  
Mihai Prunescu
Keyword(s):  
Error Bound ◽  
Common Sense ◽  
Choice Function ◽  
Continuous Functions ◽  
Ordered Sets ◽  
Choice Functions ◽  
Continuous Choice ◽  
Functions Of Two Variables ◽  
Smooth Approximations

Abstract We explore the existence of rational-valued approximation processes by continuous functions of two variables, such that the output continuously depends of the imposed error-bound. To this sake we prove that the theory of densely ordered sets with generic predicates is ℵ0- categorical. A model of the theory and a particular continuous choice-function are constructed. This function transfers to all other models by the respective isomorphisms. If some common-sense conditions are fulfilled, the processes are computable. As a byproduct, other functions with surprising properties can be constructed.

scholarly journals Approximation by Certain Linear Positive Operators of Two Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Afşin Kürşat Gazanfer ◽  
İbrahim Büyükyazıcı
Keyword(s):  
Convergence Rate ◽  
Modulus Of Continuity ◽  
Weighted Approximation ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Compact Set ◽  
Approximation Properties ◽  
Linear Positive Operators ◽  
Functions Of Two Variables

We introduce positive linear operators which are combined with the Chlodowsky and Szász type operators and study some approximation properties of these operators in the space of continuous functions of two variables on a compact set. The convergence rate of these operators are obtained by means of the modulus of continuity. And we also obtain weighted approximation properties for these positive linear operators in a weighted space of functions of two variables and find the convergence rate for these operators by using the weighted modulus of continuity.

scholarly journals On Hermite-Hadamard Type Inequalities for Coordinated Convex Functions via (p,q)-Calculus

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 698
Author(s):  
Fongchan Wannalookkhee ◽  
Kamsing Nonlaopon ◽  
Jessada Tariboon ◽  
Sotiris K. Ntouyas
Keyword(s):  
Convex Functions ◽  
Continuous Functions ◽  
Functions Of Two Variables

In this paper, we define (p,q)-integrals for continuous functions of two variables. Then, we prove the Hermite-Hadamard type inequalities for coordinated convex functions by using (p,q)-integrals. Many results obtained in this paper provide significant extensions of other related results given in the literature. Finally, we give some examples of our results.

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