Here's the question you clicked on:
cinar
I need an example of Banach space.. (10 points) Define a Banach Space and Verify that the space is Banach. (10 points) Define a operator and show that your operator is a contraction. (10 points) Apply CMT and get a conclusion. (10 points) What is the meaning of having a fixed point for the problem you are working on? (10 points) Originality.
CMT=contraction mapping theorem..
\[l_p :=\{x\in\mathbb{R}^n : ||x||_p<\infty\}\] is a known Banach space, but I'm not familiar with the details of it. I don't know about the rest of your question.
I am not familiar with this subject, but I do recall one article I saw about Contraction Mapping Theorem by Keith Conrad: http://www.math.uconn.edu/~kconrad/blurbs/analysis/contraction.pdf I apologize if it is not useful here, although I found some of his other articles useful or interesting, so maybe you can find something here? :)
Take the Banach Space R the set of real numbers with norm of x being the absolute value of X. and take the operator T(x) = 1/2 x