I have an existing table 'people_table', with a field
SELECT * FROM people_table WHERE full_name REGEXP BINARY '^[a-z]';
There's no MySQL function to do that, you have to write your own. In the following link there's an implementation:
In order to use it, first you need to create the function in the database. You can do this, for example, using MySQL Query Browser (right-click the database name and select Create new Function).
After creating the function, you can update the values in the table with a query like this:
UPDATE users SET name = CAP_FIRST(name);