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What if I do not have the double mMapView cause I put as a comment this line //mMapView = new MapView(this);
What I am missing in the code or libraries cause I still having an error in the code
ArcGISTiledMapServiceLayer cannot be resolved to a type
If you have the correct imports statements, then it sounds likely that you don't have the Jar files in your build path that contain all the Esri classes - you can add these automatically if you have the ArcGIS Runtime SDK for Android installed in Eclipse - right-click the project and choose ArcGIS Tools -> Convert to ArcGIS Android Project. If that's option is disabled, maybe your project already had this reference but it's been broken somehow, so in that case choose Fix Project Properties instead.
The doc here will tell you more about this: Integration features—ArcGIS Runtime SDK for Android.
Hope this helps,