[01] S. A. M. Mohsenialhosseini, Faculty of Mathematics, Vali-e-Asr University, Rafsanjan, Iran; Faculty of Mathematics, Yazd University, Yazd, Iran.

In this paper, we will first prove that if a Banach space has approximate fixed point property, then its dense subset also has the same property. Also, we introduce the bounded approximate fixed points property for self maps on Banach space. As application, we will prove the existence of fixed points and approximate eigenvalue to certain type of nonexpansive mappings using the existence of bounded approximate fixed points to these maps.

ε-fixed Points, Bounded ε-fixed Point, Demi-closed Map, Semi-compact Maps, Demi-compact Maps

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