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We present several sufficient conditions for normal structure of a Banach space in terms of the generalized James, von Neumann–Jordan, Zbăganu constants, and the coefficient of weak orthogonality of Sims. Our results significantly improve many known results in the literatures. A negative answer is given to the question of Llorens–Fuster [E. Llorens-Fuster, Zbganu constant and normal structure, Fixed...
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