First thank you very much for taking the trpuble to answer this.
I do have in the Settings,and always had it marked that Avast should be on the system tray.By the way,this has happened before and unfortunately NOT VERY LONG AGO.
I did and will now again uninstall Avast One and will re-install it.\I have done it before when this happened and it is not a pleasant job,my lap top is old,and I work with Win 7,so it is slow,and it is tiresome.And if it keeps happening it may force me to try other free antivirus,which I reall wouldn't like to do.I had been using Avast free and at times paid versions for many years,a well as the safe browser!
Thankl you again for your kindness!!!!