scholarly journals SOME TYPICAL PROPERTIES OF SYMMETRICALLY CONTINUOUS FUNCTIONS, SYMMETRIC FUNCTIONS AND CONTINUOUS FUNCTIONS

1995 ◽  
Vol 21 (2) ◽  
pp. 708
Author(s):  
Shi
Keyword(s):  
Symmetric Functions ◽  
Continuous Functions ◽  
Symmetrically Continuous Functions

ON LOCALLY SYMMETRIC AND SYMMETRICALLY CONTINUOUS FUNCTIONS

1980 ◽  
Vol 6 (1) ◽  
pp. 67 ◽  
Author(s):  
Kostyrko ◽  
Neubrunn ◽  
Smital ◽  
Šalát
Keyword(s):  
Continuous Functions ◽  
Symmetrically Continuous Functions

scholarly journals Remarks on uniformly symmetrically continuous functions

2016 ◽  
Vol 09 (03) ◽  
pp. 1650069
Author(s):  
Tammatada Khemaratchatakumthorn ◽  
Prapanpong Pongsriiam
Keyword(s):  
Real Line ◽  
Nonempty Subset ◽  
Continuous Functions ◽  
The Real ◽  
Definition Of ◽  
Symmetrically Continuous Functions ◽  
Uniformly Continuous

We give the definition of uniform symmetric continuity for functions defined on a nonempty subset of the real line. Then we investigate the properties of uniformly symmetrically continuous functions and compare them with those of symmetrically continuous functions and uniformly continuous functions. We obtain some characterizations of uniformly symmetrically continuous functions. Several examples are also given.

Symmetrically continuous functions

1967 ◽  
Vol 1 (4) ◽  
pp. 257-260
Author(s):  
S. P. Ponomarev
Keyword(s):  
Continuous Functions ◽  
Symmetrically Continuous Functions

scholarly journals Online Premeans and Their Computation Complexity

2021 ◽  
Vol 76 (3) ◽  
Author(s):  
Paweł Pasteczka
Keyword(s):  
Commutative Semigroup ◽  
Symmetric Functions ◽  
Continuous Functions ◽  
Regular Languages ◽  
Computation Complexity ◽  
Arithmetic Means ◽  
The Family ◽  
Additional Assumptions

AbstractWe extend some approach to the family of symmetric means (i.e. symmetric functions $$\mathscr {M} :\bigcup _{n=1}^\infty I^n \rightarrow I$$ M : ⋃ n = 1 ∞ I n → I with $$\min \le \mathscr {M}\le \max $$ min ≤ M ≤ max ; I is an interval). Namely, it is known that every symmetric mean can be written in a form $$\mathscr {M}(v_1,\dots ,v_n):=F(f(v_1)+\cdots +f(v_n))$$ M ( v 1 , ⋯ , v n ) : = F ( f ( v 1 ) + ⋯ + f ( v n ) ) , where $$f :I \rightarrow G$$ f : I → G and $$F :G \rightarrow I$$ F : G → I (G is a commutative semigroup). For $$G=\mathbb {R}^k$$ G = R k or $$G=\mathbb {R}^k \times \mathbb {Z}$$ G = R k × Z ($$k \in \mathbb {N}$$ k ∈ N ) and continuous functions f and F we obtain two series of families (depending on k). It can be treated as a measure of complexity in a family of means (this idea is inspired by theory of regular languages and algorithmics). As a result we characterize the celebrated families of quasi-arithmetic means ($$G=\mathbb {R}\times \mathbb {Z}$$ G = R × Z ) and Bajraktarević means ($$G=\mathbb {R}^2$$ G = R 2 under some additional assumptions). Moreover, we establish certain estimations of complexity for several other classical families.

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