In theory of indefinite sum, antidifference and finite calculus,  ‎the following  ‎difference ‎functional ‎equation ‎and ‎obtaining ‎its ‎some ‎special ‎solutions ‎is ‎very ‎important

‎$‎\bigtriangleup ‎F(x):=F(x+1)-F(x)=f(x) ‎\quad‎;‎\quad‎(1),‎$‎

 ‎
where‎ ‎$‎\bigtriangleup‎$ ‎is ‎the ‎forward ‎difference ‎operator and when $f$ is given and $F$ is unknown. ‎Also‎, I know that if ‎$‎‎D_f=\mathbb{R}$‎, then there exists a special solution ‎$‎‎F_0(x)$ for equation (1) and ‎ ‎we ‎have ‎the ‎general ‎solutions of ‎it ‎as ‎follows‎
‎‎‎$‎‎F=F_0+‎\lambda,‎$‎‎ ‎which ‎‎$‎‎‎\lambda$ ‎is a‎ ‎one-periodic ‎function.‎
Now‎, in my research I deal to the following functional equation

‎
$F(x+1)+F(x)=f(x)‎‎$‎‎

‎, but I don't have any knowldge about it and its soloution. ‎Any ‎one ‎can ‎help ‎me firstly, what does it call and secondly tell me some information about this‎. Thank you.