Below code may helps you for display application link of google play sore in mobile version.

For Application link :

Uri uri = Uri.parse("market://details?id=" + mContext.getPackageName());
Intent myAppLinkToMarket = new Intent(Intent.ACTION_VIEW, uri);

  try {
        startActivity(myAppLinkToMarket);

      } catch (ActivityNotFoundException e) {

        //the device hasn't installed Google Play
        Toast.makeText(Setting.this, "You don't have Google Play installed", Toast.LENGTH_LONG).show();
              }

For Developer link :

Uri uri = Uri.parse("market://search?q=pub:" + YourDeveloperName);
Intent myAppLinkToMarket = new Intent(Intent.ACTION_VIEW, uri);

            try {

                startActivity(myAppLinkToMarket);

            } catch (ActivityNotFoundException e) {

                //the device hasn't installed Google Play
                Toast.makeText(Settings.this, "You don't have Google Play installed", Toast.LENGTH_LONG).show();

            } 

Many answers here suggest to use Uri.parse("market://details?id=" + appPackageName)) to open Google Play, but I think it is insufficient in fact:

Some third-party applications can use its own intent-filters with "market://" scheme defined, thus they can process supplied Uri instead of Google Play (I experienced this situation with e.g.SnapPea application). The question is "How to open the Google Play Store?", so I assume, that you do not want to open any other application. Please also note, that e.g. app rating is only relevant in GP Store app etc...

To open Google Play AND ONLY Google Play I use this method:

public static void openAppRating(Context context) {
    // you can also use BuildConfig.APPLICATION_ID
    String appId = context.getPackageName();
    Intent rateIntent = new Intent(Intent.ACTION_VIEW,
        Uri.parse("market://details?id=" + appId));
    boolean marketFound = false;

    // find all applications able to handle our rateIntent
    final List<ResolveInfo> otherApps = context.getPackageManager()
        .queryIntentActivities(rateIntent, 0);
    for (ResolveInfo otherApp: otherApps) {
        // look for Google Play application
        if (otherApp.activityInfo.applicationInfo.packageName
                .equals("com.android.vending")) {

            ActivityInfo otherAppActivity = otherApp.activityInfo;
            ComponentName componentName = new ComponentName(
                    otherAppActivity.applicationInfo.packageName,
                    otherAppActivity.name
                    );
            // make sure it does NOT open in the stack of your activity
            rateIntent.addFlags(Intent.FLAG_ACTIVITY_NEW_TASK);
            // task reparenting if needed
            rateIntent.addFlags(Intent.FLAG_ACTIVITY_RESET_TASK_IF_NEEDED);
            // if the Google Play was already open in a search result
            //  this make sure it still go to the app page you requested
            rateIntent.addFlags(Intent.FLAG_ACTIVITY_CLEAR_TOP);
            // this make sure only the Google Play app is allowed to
            // intercept the intent
            rateIntent.setComponent(componentName);
            context.startActivity(rateIntent);
            marketFound = true;
            break;

        }
    }

    // if GP not present on device, open web browser
    if (!marketFound) {
        Intent webIntent = new Intent(Intent.ACTION_VIEW,
            Uri.parse("https://play.google.com/store/apps/details?id="+appId));
        context.startActivity(webIntent);
    }
}

The point is that when more applications beside Google Play can open our intent, app-chooser dialog is skipped and GP app is started directly.

UPDATE: Sometimes it seems that it opens GP app only, without opening the app's profile. As TrevorWiley suggested in his comment, Intent.FLAG_ACTIVITY_CLEAR_TOP could fix the problem. (I didn't test it myself yet...)

See this answer for understanding what Intent.FLAG_ACTIVITY_RESET_TASK_IF_NEEDED does.

You can do this by checking URL in shouldOverrideUrlLoading method of your WebViewClient. See below

String market_url = "market://details?id=package_name";
String website_url = "https://play.google.com/store/apps/details?id=package_name";

onCreate ()

WebView webview = (WebView) findViewById(R.id.webview);
webview.loadUrl("file:///android_asset/index.html");               // path to html
webview.setWebViewClient(new Callback());


private class Callback extends WebViewClient {
    @Override
    public boolean shouldOverrideUrlLoading(WebView view, String url) {
        if (url.equals(website_url)) {
            try {
                Intent intent = new Intent();
                intent.setAction(Intent.ACTION_VIEW);
                intent.setData(Uri.parse(market_url));
                startActivity(intent);
            } catch (ActivityNotFoundException e) {
            }
        }
        return (false);
    }
}

index.html

<a href="https://play.google.com/store/apps/details?id=package_name">App link</a>

This will always open your link in play store.