Fixed point iterations for real functions - depending on $f'(x)$?

numerical-methods recurrence-relations fixed-point-theorems fixed-point-iteration

Here are some links to the scripts of two lectures dealing with complex dynamics written by Walter Bergweiler:

http://analysis.math.uni-kiel.de/vorlesungen/kompdyn1.12/Dynamik1.pdf (german/basics)

http://analysis.math.uni-kiel.de/vorlesungen/compdyn2.16/ComplexDynamics2.pdf (english/advanced)

I hope it helps you :)


See the article on recurrence relations / difference equations here:

https://en.wikipedia.org/wiki/Recurrence_relation#Stability_of_nonlinear_first-order_recurrences

You will find the results/proofs you are interested in in any introductory textbook on difference equations.

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