Display edit link if post author is current user

If you just have to modify the author.php page, this piece of code will probably work :

<?php 

if( is_user_logged_in() && is_author(get_current_user_id()) ) {

    edit_post_link('edit', '', '');

}

?>

The first part of the conditions checks if there is a user logged.
The second one will be true if the current page is the author page of the current user.

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