Yup, same here with my iPhone5S.
The blanking applications at opening, first appeared the day after installation of iOS9, when I activated the battery saver function. Turned the funciont off and there where no blanked screens when opening applications. However, it started again the day after. Reboot -> solved the issue for a few hours, then back at it again. Reset (lock+Home button) -> solves the issue of a short while.
Now it is all the time, and I've found it is USUALLY at the first opening of an application. Only way out is the home button, and when opening the application again it works…usually. Sometimes several home button actions are needed. Worst is when an application automatically calls another application, for example my banking app, that calls up an ID applications, that blanks. There is no way to manually re-open the ID app through the home button and re-open, as it has to be called upon from the banking app to work.
So far, it's been happening randomly with all sorts of applications, apple's own as well as third party ones. Cant see any correlation to specific application services like GPS or wireless connectivity.
Sound control graphics and Control centre swipe thing works fine while the application screen is blanked, so there is something preventing the desired app graphic to show. The "gene in the bottre"-effect of opening and closing an app is visible, and just when the app reaches full screen, the blanking issue occurs.
Please fix quickly!!