Safari will not open many important apps. Need help!

My 2011 IMac updated to OSX El
Capitan Version 10.11.1 will not open websites, such as AA employee website, bank statements for my credit unions. This problem has been happening worse since the latest updates. I have been using Chrome, Yahoo to get to those sites, both on my Mac and my IPhone. Am I missing something. Supposedly the latest operating systems has the latest version of Safari. ??

Thank you for any help you can give me.

CalClerk79