On the Suzuki nonexpansive-type mappings

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It is shown that if C is a nonempty convex and weakly compact subset of a Banach space X with M(X)>1 and T:C→ C satisfies condition (C) or is continuous and satisfies condition (Cλ) for some λ∈ (0,1), then T has a fixed point. In particular, our theorem holds for uniformly nonsquare Banach spaces. A similar statement is proved for nearly uniformly noncreasy spaces.