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On von Neumann-Jordan type constant and sufficient conditions for fixed points of multivalued nonexpansive mappings

In the present paper, we give some geometric conditions in terms of the von Neumann-Jordan type constant and the Dominguez-Benavides' coefficient which in turn are sufficient for the existence of fixed points of multivalued nonexpansive and 1-χ-contractive nonself mappings satisfying the inwardness condition and normal structure in a reflexive Banach space. Our main results improve some well known results in the recent literature.