In the previous works ( Parts I and II), running exprssions written in terms of 1 to 9 and 9 to 1 or 9 to 0 separated by one or more equality signs. Each digit appears once. Along with basic operations, factorial and square-root are also used. These types of expressions are understood as running expressions. This work brings running expressions with double and triple equality signs using Fibonacci sequence numbers along with basic operations. The work is up to 3 digits in increasing and decreasing orders. For 4 digits onwards the results are still under preparation. See below some examples and link to download the work.