Related papers: The skew James type constant in Banach spaces

Recently, the von Neumann-Jordan type constants C(X) has defined by Takahashi. A new skew generalized constant Cp({\lambda},\mu,X) based on C(X) constant is given in this paper. First, we will obtain some basic properties of this new…

We study the James constant $J(\mathbb{X})$, an important geometric quantity associated with a normed space $ \mathbb{X} $, and explore its connection with isosceles orthogonality $ \perp_I. $ The James constant is defined as $J(\mathbb{X})…

In this article, we introduce a novel geometric constant $L_X(t)$, which provides an equivalent definition of the von Neumann-Jordan constant from an orthogonal perspective. First, we present some fundamental properties of the constant…

In this paper, based on Birkhoff orthogonality, we introduce two geometric constants $\boldsymbol{A}_{\boldsymbol{t}}^{\boldsymbol{B}}(\boldsymbol{X})$ and $\boldsymbol{D}_{\boldsymbol{t}}^{\boldsymbol{B}}(\boldsymbol{X})$ in Banach spaces,…

In this paper, combined with the P-angle function of Banach spaces and the geometric constants that can characterize Hilbert spaces, the new angular geometric constant is defined. Firstly, this paper explores the basic properties of the new…

This paper defines the skew von Neumann constant in quasi-Banach spaces. Meanwhile, we obtain two constants. It presents the upper and lower bounds of two constants. Subsequently, it deduces the lower bound of the skew von Neumann constant…

This paper contains a study of the separable form $J_s(\cdot)$ of the classical Jung constant. We first establish, following Davis \cite{davis}, that a Banach space $X$ is $1$-separably injective if and only if $J_s(X)=1$. This…

We present some new results on the symmetric Kottman's constant $K^s(X)$ of a Banach space $X$ and its relationship with the Kottman constant. We show that $K^s(X)>1$, for every infinite-dimensional Banach space, thereby solving a problem…

In this paper, we build upon the TX constant that was introduced by Alonso and Llorens-Fuster in 2008. Through the incorporation of suitable parameters, we have successfully generalized the aforementioned constant into two novel forms of…

We show that the Kottman constant $K(\cdot)$, together with its symmetric and finite variations, is continuous with respect to the Kadets metric, and they are log-convex, hence continuous, with respect to the interpolation parameter in a…

This article delves into an exploration of two innovative constants, namely DW(X,{\alpha},\b{eta}) and DWB (X,{\alpha},\b{eta}), both of which constitute extensions of the Dunkl-Williams constant. We derive both the upper and lower bounds…

The main aim of this work is to give a general approach to the celebrated Kahane-Salem-Zygmund inequalities. We prove estimates for exponential Orlicz norms of averages $\sup_{1\le j \leq N} \big |\sum_{1 \leq i \leq K}\gamma_i(\cdot)…

The paper emphasizes the property of stability for skew-evolution semiflows on Banach spaces, defined by means of evolution semiflows and evolution cocycles and which generalize the concept introduced by us in a previous paper. There are…

In this paper, we define a new geometric constant based on isosceles orthogonality, denoted by . Through research, we find that this constant is the equivalent p-th von Neumann Jordan constant in the sense of isosceles orthogonality. First,…

The class J of simultaneously almost transitive, uniformly convex and uniformly smooth Banach spaces is characterized in terms of convex-transitivity and weak geometry of the norm.

We investigate possible quantifications of R. C. James' classical work on bases and reflexivity of Banach spaces. By introducing new quantities measuring how far a basic sequence is from being shrinking and/or boundedly complete, we prove…

The general problem we address is to develop new methods in the study of projection constants of Banach spaces of multivariate polynomials. The relative projection constant $\boldsymbol{\lambda}(X,Y)$ of a subspace $X$ of a Banach $Y$ is…

A Banach space $X$ is said to have the $\mathsf{SVM}$ (stability of vector measures) property if there exists a constant $v<\infty$ such that for any algebra of sets $\mathcal F$, and any function $\nu\colon\mathcal F\to X$ satisfying…

Let X and Y be Banach spaces and F a subset of B_{Y^*}. Endow Y with the topology \tau_F of pointwise convergence on F. Let T: X^* \to Y be a bounded linear operator which is (w^*, \tau_F) continuous. Assume that every vector in the range…

There are discussed some modifications of n-th von Neumann-Jordan constant considered by M. Kato, Y. Takahashi and K. Hashimoto. We study, among others, upper, lower, upper modified and lower modified n-th von Neumann-Jordan constant and…