Generalizations of the Intermediate Value Theorem for Approximating Fixed Points and Zeros of Continuous Functions

2020 ◽  
pp. 223-238
Author(s):  
Michael N. Vrahatis
Keyword(s):  
Fixed Points ◽  
Continuous Functions ◽  
Intermediate Value Theorem ◽  
Intermediate Value

3. Thinking continuously

2019 ◽  
pp. 48-63
Author(s):  
Richard Earl
Keyword(s):  
Real Variable ◽  
Continuous Functions ◽  
Boundedness Theorem ◽  
Intermediate Value Theorem ◽  
Discontinuous Functions ◽  
Intermediate Value

Many topologists might choose to describe their subject as the study of continuity. There are continuous and discontinuous functions in our everyday routines. ‘Thinking continuously’ aims to provide a more rigorous sense of what continuity entails for real-valued functions of a real variable. It focuses on functions having a single numerical input and a single numerical output. The properties of continuous functions are considered and the boundedness theorem and intermediate value theorem are also explained.

scholarly journals Stirring our way to Sharkovsky's theorem

1997 ◽  
Vol 56 (3) ◽  
pp. 453-458
Author(s):  
Seth Patinkin
Keyword(s):  
Topological Space ◽  
Periodic Point ◽  
Real Line ◽  
Continuous Functions ◽  
Cycle Structure ◽  
Intermediate Value Theorem ◽  
The Real ◽  
Continuous Map ◽  
Sharkovsky's Theorem ◽  
Intermediate Value

The periodic-point or cycle structure of a continuous map of a topological space has been a subject of great interest since A.N. Sharkovsky completely explained the hierarchy of periodic orders of a continuous map f: R → R, where R is the real line. In this paper the topological idea of “stirring” is invoked in an effort to obtain a transparent proof of a generalisation of Sharkovsky's Theorem to continuous functions f: I → I where I is any interval. The stirring approach avoids all graph-theoretical and symbolic abstraction of the problem in favour of a more concrete intermediate-value-theorem-oriented analysis of cycles inside an interval.

scholarly journals On some properties of the conformable fractional derivative

2020 ◽  
Vol 6 (2) ◽  
pp. 210-217
Author(s):  
Radouane Azennar ◽  
Driss Mentagui
Keyword(s):  
Fractional Derivative ◽  
Conformable Fractional Derivative ◽  
Intermediate Value Theorem ◽  
Definition Of ◽  
Intermediate Value

AbstractIn this paper, we prove that the intermediate value theorem remains true for the conformable fractional derivative and we prove some useful results using the definition of conformable fractional derivative given in R. Khalil, M. Al Horani, A. Yousef, M. Sababhehb [4].

Bernoulli convolutions and an intermediate value theorem for entropies ofK-partitions

2002 ◽  
Vol 87 (1) ◽  
pp. 337-367 ◽  
Author(s):  
Elon Lindenstrauss ◽  
Yuval Peres ◽  
Wilhelm Schlag
Keyword(s):  
Intermediate Value Theorem ◽  
Bernoulli Convolutions ◽  
Intermediate Value
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