scholarly journals Approximating fixed points for continuous functions on an arbitrary interval

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Prasit Cholamjiak ◽  
Nattawut Pholasa
Keyword(s):  
Fixed Points ◽  
Continuous Functions ◽  
Arbitrary Interval

Chaotic Dynamics of Composition Operators on the Space of Continuous Functions

2017 ◽  
Vol 27 (06) ◽  
pp. 1750084 ◽  
Author(s):  
Zongbin Yin
Keyword(s):  
Fixed Points ◽  
Composition Operator ◽  
Chaotic Dynamics ◽  
Composition Operators ◽  
Continuous Functions ◽  
Space Of Continuous Functions ◽  
Distributional Chaos ◽  
Long Time ◽  
Topologically Mixing ◽  
Mixing Property

In this paper, the chaotic dynamics of composition operators on the space of real-valued continuous functions is investigated. It is proved that the hypercyclicity, topologically mixing property, Devaney chaos, frequent hypercyclicity and the specification property of the composition operator are equivalent to each other and are stronger than dense distributional chaos. Moreover, the composition operator [Formula: see text] exhibits dense Li–Yorke chaos if and only if it is densely distributionally chaotic, if and only if the symbol [Formula: see text] admits no fixed points. Finally, the long-time behaviors of the composition operator with affine symbol are classified in detail.

scholarly journals Digital fixed points, approximate fixed points, and universal functions

2016 ◽  
Vol 17 (2) ◽  
pp. 159 ◽  
Author(s):  
Laurence Boxer ◽  
Ozgur Ege ◽  
Ismet Karaca ◽  
Jonathan Lopez ◽  
Joel Louwsma
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Digital Images ◽  
Continuous Functions ◽  
Universal Functions ◽  
Approximate Fixed Point ◽  
Fixed Point Properties ◽  
Digitally Continuous ◽  
Approximate Fixed Point Property ◽  
The Relationship

A. Rosenfeld [23] introduced the notion of a digitally continuous function between digital images, and showed that although digital images need not have fixed point properties analogous to those of the Euclidean spaces modeled by the images, there often are approximate fixed point properties of such images. In the current paper, we obtain additional results concerning fixed points and approximate fixed points of digitally continuous functions. Among these are several results concerning the relationship between universal functions and the approximate fixed point property (AFPP).

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