70 Years of asymptotic fixed point theory

2015 ◽  
Vol 17 (1) ◽  
pp. 3-21 ◽  
Author(s):  
Heinrich Steinlein
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Asymptotic Fixed Point ◽  
Asymptotic Fixed Point Theory

On the Theorems of Borsuk-Ulam and Ljusternik-Schnirelmann-Borsuk

1984 ◽  
Vol 27 (2) ◽  
pp. 192-204 ◽  
Author(s):  
H. Steinlein
Keyword(s):  
Fixed Point ◽  
Positive Integer ◽  
Fixed Points ◽  
Prime Number ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Asymptotic Fixed Point ◽  
Asymptotic Fixed Point Theory

AbstractLet p ≥ 3 be a prime number and m a positive integer, and let S be the sphere S(m-1)(p-1)-1. Let f:S→S be a map without fixed points and with fp = idS. We show that there exists an h: S→ℝm with h(x) ≠ h(f(x)) for all x ∈ S. From this we conclude that there exists a closed cover U1,…, U4m of S with Uinf(Ui) = Ø for i = 1,…, 4m. We apply these results to Borsuk-Ulam and Ljusternik-Schnirelmann-Borsuk theorems in the framework of the sectional category and to a problem in asymptotic fixed point theory.

Modeling the dynamics of hepatitis E via the Caputo–Fabrizio derivative

2019 ◽  
Vol 14 (3) ◽  
pp. 311 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Zakia Hammouch ◽  
Dumitru Baleanu
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Numerical Scheme ◽  
Arbitrary Order ◽  
Fixed Point Theory ◽  
Hepatitis E ◽  
Point Theory ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Essential Properties

A virus that causes hepatitis E is known as (HEV) and regarded on of the reason for lever inflammation. In mathematical aspects a very low attention has been paid to HEV dynamics. Therefore, the present work explores the HEV dynamics in fractional derivative. The Caputo–Fabriizo derivative is used to study the dynamics of HEV. First, the essential properties of the model will be presented and then describe the HEV model with CF derivative. Application of fixed point theory is used to obtain the existence and uniqueness results associated to the model. By using Adams–Bashfirth numerical scheme the solution is obtained. Some numerical results and tables for arbitrary order derivative are presented.

scholarly journals A new method in fixed point theory

1960 ◽  
Vol 34 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Richard G. Swan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
New Method
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