Such things are much easier, faster and more convenient to do in the vector . To draw a similar background, you need literally 2 minutes. It will look great on any screens and most of the problems associated with this simply disappear.
Under the link you can download a ready .xml background in vector, drawn from your picture.

HOW TO DO IT?
Step 1. In any vector editor, such as Adobe Illustrator or CorelDraw , draw a rectangle and adjust the corners / fill / gradient / other. With rectangles it is quite simple, but for more complex things, you have to spend a couple of hours to master the basic features of the program.
Step 2. Export the result in svg format. In order for Android Studio to properly eat your file, its parameters must be as follows:
Стили - Атрибуты представления Шрифт - SVG Изображения - Встроить ID объектов - Имена слоев Точность - 2 Уменьшение файла - включено Адаптивность - включено
Step 3. In Android Studio, add your file via Vector Asset . Select the item Local file and specify the path to it. Click the Finish button - everything is ready, the file can be used.
TIPS
Never use a stroke in svg . If you need a stroke, then before exporting, translate it into curves.
Do not use raster effects like shadows or glows. They are easy to draw vector. There are many tutorials on this topic.
If your vector uses a simple linear or circular gradient, it is better to save the file with a regular fill. And configure the gradient already in Android Studio . This will allow, if necessary, to quickly change its colors directly in the IDE . Here is a well and clearly described the work with a circular gradient. With linear everything is simple - startColor , centerColor , endColor .
This can be done not only with the background for buttons and items. Any icons and custom interface elements saved in a vector make life much easier.