GUITexture and Touch Input

You just need to check hitTest of GUITexture with Touch input. If HitTest is true then check if TouchPhase is Began (OnMouseDown) or stationary(OnMouseEnter) or Ended (OnMouseUp).

 public class TouchExample : MonoBehaviour 

{

 public GUITexture myImg;
 
 // Update is called once per frame
 void Update () 
 {
     if (myImg.HitTest(Input.GetTouch(0).position))
     {
         if(Input.GetTouch(0).phase==TouchPhase.Began)
         {
             print("Touch has began on image");
         }
         if(Input.GetTouch(0).phase==TouchPhase.Stationary)
         {
             print("Touch is on image");
         }
         if(Input.GetTouch(0).phase==TouchPhase.Moved)
         {
             print("Touch is moving on image");
         }
         if(Input.GetTouch(0).phase==TouchPhase.Ended)
         {
             print("Touch has been ended on image");
         }
     }
 }