THE GENERALIZED VON NEUMMAN-JORDAN CONSTANT AND FIXED POINTS OF MULTIVALUED NONEXPANSIVE MAPPINGS IN BANACH SPACES

Abstract

Recently, a new geometric constant called generalized von Neumman-Jordan constant was introduced. In this work, we give some sufficient conditions for the (DL)-condition and property (D) in terms of this new constant and many coefficients namely the weakly convergent sequence coefficient, the normal structure coefficient, the coefficient of weak orthogonality and the generalized Garcเธฃยเธขเธ”เธฃยเธขเธ‘a-Falset coefficient. As consequences, we obtain several sufficient conditions which imply the existence of fixed points for multivalued nonexpansive mappings and normal structure in Banach spaces. The obtained results generalize and unify some known results in the recent literature.