FIXED POINT THEOREMS FOR NONEXPANSIVE MAPPINGS IN MODULAR SPACES
Poom Kumam · Czech digital mathematics library · 2004
Abstract. 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 ρ is a convex, ρ-complete modular space satisfying the Fatou property and ρr-uniformly convex for all r> 0, C a convex, ρ-closed, ρ-bounded subset of Xρ, T: C → C a ρ-nonexpansive mapping, then T has a fixed point. 1.