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Authors define w∗ nearly dentable Banach space. Authors study Radon-Nikodym property, approximative compactness and continuity metric projector operator in w∗ nearly dentable space. Moreover, authors obtain some examples of w∗ nearly dentable space in Orlicz function spaces. Finally, by the method of geometry of Banach spaces, authors give important applications of w∗ nearly dentability in generalized inverse theory of Banach space.