Follow Player in 2D Game

At present I am working on 2d side scrolling game. I want camera follow for player movement only in horizontal movement. Right now I have written this type of target following script

 public class SmoothFollow : MonoBehaviour
 {
     public Transform target;
     public float smoothness = 10f;
     private Vector3 targetInitialPos;
 
     void OnEnable ()
     {
         target = null;
     }
 
     void Update ()
     {
         if (!target) {
             target = GameObject.Find ("MrJump").transform;
             targetInitialPos = target.position;
         } else {
 
             Vector3 cameraPosition = target.position - targetInitialPos;
             cameraPosition.y = 0f;
             cameraPosition.z = -10f;
 //            transform.position = cameraPosition;
             transform.position = Vector3.Lerp (transform.position, cameraPosition, Time.deltaTime * smoothness);
 
         }
     }
 }

If I directly apply cameraPosition to camera transform then it stuttering in mobile devices. So that I used lerp for this purpose but didn't got success in that also. I have attached small video also to represent my problem correctly.

Camera Stuttering Video

Using above code it shows jerky movement of camera. Not smoother one that I want. Please give some suggestion in this.