Notices for WP 4.3

There is a big update coming soon: https://demo.acosmin.com/D_justwrite it will solve those issues.

If you are in a hurry you can open ../acosmin/widgets/
custom-featured-posts-widget.php
custom-popular-posts-widget.php
custom-recent-posts-widget.php
custom-tabs-widget.php
default-social-buttons-widget.php

and where it says at the beginning:
function AC_Featured_Posts_Widget() {
replace with:
function __construct() {

I think your instructions are wrong.

function AC_Featured_Posts_Widget() {

is only in one php file. Apparently other functions in other files need to be replaced ?

function AC_Featured_Posts_Widget() {
function AC_Popular_Posts_Widget() {
function AC_Recent_Posts_Widget() {
function AC_Tabs_Widget() {
function ac_social_buttons_widget()  {

in all those files

Yes but in those files there is no

function AC_Featured_Posts_Widget() {

there is a different fuction name. Apparently that needs to be replaced.

?? I wrote above you should replace them with:
function __construct() {

All good now.

And the new update looks excellent, just try not to over-load it with effects and transitions. A trap a lot of theme devs fall into.