On New Moduli Related to the Generalization of the Parallelogram Law

Abstract We shall introduce a new geometric constant %$L^{\prime }_{\mathrm {YJ}}(\lambda ,\mu ,X)%$ based on a generalization of the parallelogram law, which was proposed by Moslehian and Rassias. We first discuss some basic properties of this new coefficient. Next, it is shown that, for a Banach s...
Ausführliche Beschreibung

Abstract We shall introduce a new geometric constant %$L^{\prime }_{\mathrm {YJ}}(\lambda ,\mu ,X)%$ based on a generalization of the parallelogram law, which was proposed by Moslehian and Rassias. We first discuss some basic properties of this new coefficient. Next, it is shown that, for a Banach space, %$L^{\prime }_{\mathrm {YJ}}(\lambda ,\mu ,X)%$ becomes 1 if and only if the norm is induced by an inner product. Moreover, some sufficient conditions which imply normal structure are presented. Finally, we describe some relations between the well-known geometric constants and %$L^{\prime }_{\mathrm {YJ}}(\lambda , \mu ,X)%$ through some inequalities. Ausführliche Beschreibung