You can use an AppImage app without being a root user and with all required libraries included in the file.

(From its Wiki) An AppImage is a downloadable file for Linux that contains an application and everything the application needs to run (e.g., libraries, icons, fonts, translations, etc.) that cannot be reasonably expected to be part of each target system.

Search for an AppImage version of your chosen application

There is a list of AppImage apps in AppImageHub but if your app is not there, it does not mean the app does not have an AppImage version (e.g.: tmux has an AppImage version but it does not appear on the list). You can use a search engine to find it.

Download and run

Download the file, make it executable (chmod u+x app.AppImage) and run (./app.AppImage). You do not need superuser privileges to do it. You can copy the file to your local PATH so you can run the app from any folder without typing its path.