Delete Post From front Page ( With Wp-admin restriction )

am using this function to delete post from front

// Delete from Front-End Link

function wp_delete_post_link($link = 'Delete This', $before="", $after="", $title="Move this item to the Trash", $cssClass="delete-post") {
    global $post;
    if ( $post->post_type == 'page' ) {
        if ( !current_user_can( 'edit_page' ) )
            return;
    } else {
        if ( !current_user_can( 'edit_post' ) )
            return;
    }
    $delLink = wp_nonce_url( site_url() . "/wp-admin/post.php?action=trash&post=" . $post->ID, 'trash-' . $post->post_type . '_' . $post->ID);
    $link = '<a class="' . $cssClass . '" href="' . $delLink . '" onclick="javascript:if(!confirm(\'Are you sure you want to move this item to trash?\')) return false;" title="'.$title.'" />'.$link."</a>";
    return $before . $link . $after;
}

its work 100% but am using function to restrict no admin to access wp-admin, using this function :

function restrict_admin(){
//if not administrator, kill WordPress execution and provide a message
    if ( ! current_user_can( 'create_users' ) ) {
        wp_die( __('You are not allowed to access this part of the site') );
    }
}
add_action( 'admin_init', 'restrict_admin', 1 );

my problem , how can i allow user ( not admin ) to delete his post own post ?

If you like, that users only can delete his own post, then it is important, that check for the ID of the user and the Author-ID to the post. The follow source example add a Trash button to the admin bar, that the users can easily delete his own post.

The key is the function get_queried_object(). This object stored all values to the post on the front end and you can check to the user id, there is logged in – get_current_user_id(). Also important for a strict comparison is, that you set all values to the same type, like integer.

Also is it possible to use the WP core function current_user_can() with the second param to identifier the rights to each post: current_user_can('edit_post', 123) this check the capability to the post with the ID 123. Maybe a little bid easier as the check about the author object and the post object.

Also useful in my example, that you nit must use the global $post.

add_action( 'admin_bar_menu', 'fb_add_admin_bar_trash_menu', 35 );
function fb_add_admin_bar_trash_menu() {

  if ( ! is_super_admin() || ! is_admin_bar_showing() )
      return;

  $current_object = get_queried_object();

  // check, is the objekt with the value readable
  if ( ! isset( $current_object->post_author ) )
      return;

  // check, if the user id the same as the author-id if the current post
  if ( (int) $current_object->post_author !== (int) get_current_user_id() )
      return;

  if ( empty( $current_object ) )
      return;

  if ( ! empty( $current_object->post_type ) && 
     ( $post_type_object = get_post_type_object( $current_object->post_type ) ) && 
     current_user_can( $post_type_object->cap->edit_post, $current_object->ID ) 
  ) {
    global $wp_admin_bar;

    $wp_admin_bar->add_menu( 
        array(
            'id'    => 'delete', 
            'title' => __( 'Move to Trash' ), 
            'href'  => get_delete_post_link( $current_object->term_id ) 
        ) 
    );
  }
}

For the non access to the admin area of non admin is it easier to write a small function include a rewrite, not a hard die. Use the WordPress function wp_redirect() to rewrite to a specific url or frontend.

add_action( 'admin_init', 'fb_redirect_to_frontend' );
function fb_redirect_to_frontend() {

    if ( ! current_user_can( 'remove_users' ) )
        wp_redirect( site_url() );
}