Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 24 (2017), No. 3, 917--925Copyright Heldermann Verlag 2017 On Rectangular Constant in Normed Linear Spaces Kallol Paul Dept. of Mathematics, Jadavpur University, Kolkata 700032, India kalloldada@gmail.com Puja Ghosh Dept. of Mathematics, Jadavpur University, Kolkata 700032, India ghosh.puja1988@gmail.com Debmalya Sain Dept. of Mathematics, Jadavpur University, Kolkata 700032, India saindebmalya@gmail.com [Abstract-pdf] We study the properties of rectangular constant $\mu(\mathbb{X})$ in a normed linear space $\mathbb{X}$. We prove that $\mu(\mathbb{X}) = 3$ if and only if the unit sphere contains a straight line segment of length 2. In fact, we prove that the rectangular modulus attains its upper bound if and only if the unit sphere contains a straight line segment of length 2. We prove that if the dimension of the space $\mathbb{X}$ is finite then $\mu(\mathbb{X})$ is attained. We also find a necessary and sufficient condition for a normed linear space to be an inner product space in terms of conditions involving rectangular constant. Keywords: Birkhoff-James Orthogonality, rectangular constant. MSC: 46B20; 47A30 [ Fulltext-pdf  (109  KB)] for subscribers only.