SHELL

git push rejected

Just pull repository first and then try to push again
git pull --rebase remote_repo
git push origin remote_repo

git push -u rejected

git pull origin master 
git push -u origin master

git push origin branch rejected

#fetching remote 'feature/my_feature_branch' branch to the 'tmp' local branch 
git fetch origin feature/my_feature_branch:tmp

#rebasing on local 'tmp' branch
git rebase tmp

#pushing local changes to the remote
git push origin HEAD:feature/my_feature_branch

#removing temporary created 'tmp' branch
git branch -D tmp