I am using 3rd party to send and receive SMS, which includes text plus url of image. Is there any way that latest smartphones shows picture instead of link? Like the downloadable content.
If you want to show the image content from the URL all you can do is write a notification Application Which will read from the SMS that you are sending and (using the thirdparty number from which you are sending the sms) and notify the user with image (by reading the content of the SMS and downloading it from URL). 
But then all your users will have to download your app.and will need read permissions for SMS.
SMS with picture link