I am using a new feature of SpreadSheet in Google Sheets: "Named and protected ranges". In this range of protected cells, I use arithmetic built-in functions and my own written functions. The trigger to run my functions is on edit spreadsheet.
Users with write permissions, sharing the link of the spreadsheet, can't properly run my functions for permissions problem while built-in functions run properly.
Own can I grant permissions for my functions to run as Google Sheets built-in functions.
Built-in functions (Google Spreadsheet functions) have nothing to do with your triggered functions (made by you). You're complicating the explanation with 2 things that have nothing in common. Of course Google functions will work!
Please explain better your functions, are they triggered by what? onEdit, onOpen, a menu? What protected ranges have to do with it? Does your functions work if you remove the protection of your ranges?
[edit]
Simple event handlers (like onEdit) have limited permissions by design, you probably need to set a installable on edit trigger. Please check out this other answer I gave.
来源：https://stackoverflow.com/questions/11982373/permissions-for-custom-functions-in-spreadsheets