### Fixed point theorems for nonexpansive mappings in modular spaces

In this paper, we extend several concepts from geometry of Banach spaces to modular spaces. With a careful generalization, we can cover all corresponding results in the former setting. Main result we prove says that if $\rho $ is a convex, $\rho $-complete modular space satisfying the Fatou property and ${\rho}_{r}$-uniformly convex for all $r>0$, C a convex, $\rho $-closed, $\rho $-bounded subset of ${X}_{\rho}$, $T:C\to C$ a $\rho $-nonexpansive mapping, then $T$ has a fixed point.