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MBA IT, Mater in Science and Technology
Devry
Jul-1996 - Jul-2000
Professor
Devry University
Mar-2010 - Oct-2016
This problem is a mathematical equation demonstration for a management course.
In Fractal geometry, “Fix point” is defined as:
Let f: XX be a transformation on a metric space.
x
f (¿¿ f )=x f
¿ A point xf ∈ X such that is called the fixed point of the transformation And “contraction mapping” is defined as:
Definition 6.1: A transformation f: X X on a metric space (X, d) is called contractive or
“contraction mapping” if there is a constant 0<s<1 such that
d ( f ( x ) , f ( y ) ) ≤ s ., ∀ x , y ∈ X
Any such number s is called a scale factor for f
{Note: x & y are two members of X and d (x , y) represents the distance between x & y} In other words, in every iteration, transformation f brings all points closer to each other (and to
the fractal attractor), by a factor of s, preventing them from going to infinity. All points
eventually converge to & dance around the “Fixed Point (F)”.
Show how you can use this concept to better explain the role of “effective intervention” for
conflict resolution. What is “s” and what is “F” in this case? Start with opinion x (from member
X) and opinion y (from member Y) and apply f(x) & f(y), with scale factor s & show what
happens after a few iterations, knowing s<1. Also discuss what happens when s>1 & what cases
it.