scholarly journals Fixed points of maps on the space of rational functions

2006 ◽  
Author(s):  
Edward Mosteig
Keyword(s):  
Fixed Points ◽  
Rational Functions

Fixed points of rational functions satisfying the Carlitz property

2019 ◽  
Vol 30 (5) ◽  
pp. 417-439 ◽  
Author(s):  
Kaitlyn Chubb ◽  
Daniel Panario ◽  
Qiang Wang
Keyword(s):  
Fixed Points ◽  
Rational Functions

HOW IS THE DYNAMICS OF KÖNIG ITERATION FUNCTIONS AFFECTED BY THEIR ADDITIONAL FIXED POINTS?

Fractals ◽  
1999 ◽  
Vol 07 (03) ◽  
pp. 327-334 ◽  
Author(s):  
V. DRAKOPOULOS
Keyword(s):  
Fixed Points ◽  
Rational Functions ◽  
Parameter Family ◽  
Quadratic Polynomials ◽  
Iteration Functions ◽  
Extraneous Fixed Points ◽  
Roots Of Equations ◽  
The One ◽  
Cubic Polynomials ◽  
Raphson Method

König iteration functions are a generalization of Newton–Raphson method to determine roots of equations. These higher-degree rational functions possess additional fixed points, which are generally different from the desired roots. We first prove two new results: firstly, about these extraneous fixed points and, secondly, about the Julia sets of the König functions associated with the one-parameter family of quadratic polynomials. Then, after finding all the critical points of the König functions as applied to a one-parameter family of cubic polynomials, we examine the orbits of the ones available for convergence to an attracting periodic cycle, should such a cycle exist.

INFINITE BASINS OF JULIA SETS

2008 ◽  
Vol 18 (10) ◽  
pp. 3169-3173
Author(s):  
FİGEN ÇİLİNGİR
Keyword(s):  
Entire Function ◽  
Fixed Points ◽  
Newton’S Method ◽  
Newton's Method ◽  
Julia Sets ◽  
Rational Functions ◽  
Complex Parameter

The goal of this paper is to investigate the iterative behavior of a particular class of rational functions which arise from Newton's method applied to the entire function (z2 + c)eQ(z) where c is a complex parameter and Q is a nonconstant polynomial with deg(Q) ≤ 2. In particular, the basins of attracting fixed points will be described.

On $\alpha$-nonexpansive mapping and fixed-points in Banach spaces

2018 ◽  
Vol 2018 (-) ◽  
Author(s):  
Prondanai Kaskasem ◽  
Chakkrid Klin-eam ◽  
Suthep Suantai
Keyword(s):  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Banach Spaces

Fixed Points of Sequences of Mappings

2018 ◽  
Vol 2018 (-) ◽  
Author(s):  
C. Ganesa Moorthy ◽  
S. Iruthaya Raj
Keyword(s):  
Fixed Points
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