In recent times, many constants in Banach spaces have been defined and/or studied.
Relations and inequalities among them (sometimes very complicated) have been indicated …

We consider the triangles with vertices x,− x and y where x, y are points on the unit sphere of
a normed space. Using the geometric means of the variable lengths of the sides of these …

Let CNJ (X) and J (X) be the von Neumann–Jordan and James constants of a Banach space
X, respectively. We shall show that CNJ (X)⩽ J (X), where equality holds if and only if X is not …

We introduce a new geometric constant CNJ (p)(X) C_NJ^(p)(X) for a Banach space X,
called a generalized von Neumann-Jordan constant. Next, it is shown that 1≤ CNJ (p)(X)≤ …

Let X be a non-trivial Banach space. L. Maligranda conjectured CNJ (X)≤ 1+ J (X) 2/4 for
James constant J (X) and von Neumann–Jordan constant CNJ (X) for X. Recently, J. Alonso …

Geometric constant is one of the important tools to study geometric properties of Banach
spaces. In this paper, we will introduce two new geometric constants JL (X) and YJ (X) in …

Inspired by Clarkson's inequalities for $ L^ p $ and continuing work from\cite {CR}, this paper
computes the optimal constant $ C $ in the weak parallelogram laws $$\| f+ g\|^ r+ C\| fg …

The weakly convergent sequence coefficient \rmWCS(X) is estimated by the James type
constant J_X,t(τ), Jordan-von Neumann type constant C_t(X) and the Domínguez Benavides …

In this paper, we present some sufficient conditions for the uniform normal structure of
Banach spaces and their dual spaces. More precisely, many known conditions implying the …

We shall introduce a new geometric constant L^ ′ _ YJ (λ, μ, X) L YJ′(λ, μ, X) based on a
generalization of the parallelogram law, which was proposed by Moslehian and Rassias …