Q:

To display the Back button at the top right corner while playing the video

Below I done a code and use menu for creating the back button.
VideoFragment.java:
public class VideoFragment extends BaseFragment implements OnItemClickListener {

@Override
    public View onCreateView(LayoutInflater inflater, ViewGroup container,
            Bundle savedInstanceState) {

        this.setHasOptionsMenu(true);

        return view;
    }

    @Override
    public void onCreateOptionsMenu(Menu menu, MenuInflater inflater) {
        super.onCreateOptionsMenu(menu, inflater);
        menu.clear();
        inflater.inflate(R.menu.main_menu, menu);

    }
    @Override
    public boolean onOptionsItemSelected(MenuItem item) {
        switch (item.getItemId()) {
        case R.id.menuitem_back:
            getActivity().onBackPressed();
            break;
        default:
            break;
        }
        return true;

    }
}

YouTubePlayActivity.java:
public class YoutubePlayActivity extends YouTubeFailureRecoveryActivity{
    public static final String DEVELOPER_KEY = "key here";
    private String videoId;
    private YouTubePlayerView youTubeView;
    @Override
    protected void onCreate(Bundle arg0) {
        super.onCreate(arg0);

        setContentView(R.layout.youtube_play);
        Bundle bundle= getIntent().getExtras();
        videoId= bundle.getString("videoid");

        FrameLayout frameLayout=(FrameLayout) findViewById(R.id.youtube_view);
        youTubeView = new YouTubePlayerView(this);
        frameLayout.addView(youTubeView);
        youTubeView.initialize(DEVELOPER_KEY, this);

        ((TextView) findViewById(R.id.header_title)).setText(bundle.getString("title"));

        findViewById(R.id.blog_back).setOnClickListener(new OnClickListener() {

            @Override
            public void onClick(View v) {
                onBackPressed();

            }
        });
    }

    @Override
      public void onInitializationSuccess(YouTubePlayer.Provider provider, YouTubePlayer player,
          boolean wasRestored) {
        if (!wasRestored) {
        try {
            if(videoId!=null){
                //2GPfZYwYZoQ
                player.cueVideo(videoId);
            }else{
                Toast.makeText(getApplicationContext(), "Not a Valid Youtube Video", Toast.LENGTH_SHORT).show();
            }
        } catch (Exception e) {
            Toast.makeText(getApplicationContext(), "Not a Valid Youtube Video", Toast.LENGTH_SHORT).show();
        }   

        }
      }

      @Override
      protected YouTubePlayer.Provider getYouTubePlayerProvider() {
        return youTubeView;
      }

}

In res/menu: 
main_menu.xml:
<menu xmlns:android="http://schemas.android.com/apk/res/android" >

    <item
        android:id="@+id/menuitem_back"
        android:showAsAction="always"
        android:title="@string/back">
    </item>

</menu>  

I get a back button at the top right corner of the father house.
I got a problem because I have to get the back button at the top right corner while playing the video. 
More over I just click and play the video.Now back button wasn't displayed at the top right corner of the father house.

A:

You have two ways for providing back button functionality. One is already done for you via the phone's back button. The other way even interacts with the ActionBar. Why reinvent the wheel?
I suggest you read the docs on how to provide Up Navigation in your app.

