Shayes13

I have a 2005 mazda 3. When started it idles high as normal for a cold engine, then the rpms drop and fluctuate until it eventually dies. Although when the rps drop, if i just hit the gas one time to reach 1500rpms it runs fine. I dont have to continuously hit the gas. Just one time. Check engine light is on. It reads o2 sensor bank 1 sensor 1. I replaced it, but the light came back on for the same thing. Ive replaced the spark plugs and ran fuel injector cleaner. Its starting to get colder outside so my problem is getting worse. Help