The James–Schreier spaces Vp, where 1 6 p < ∞, were recently introduced by Bird and Laustsen [5] as an amalgamation of James’ quasi-reflexive Banach space on the one hand and Schreier’s Banach space giving a counterexample to the Banach–Saks property on the other. The purpose of this note is to answer some questions left open in [5]. Specifically, we prove that (i) the standard Schauder basis f...

It is proved that orthogonal convexity defined by A. JimenezMelado and E. Llorens-F'uster implies the weak Banach-Saks property. Relations between orthogonal convexity and another geometric properties, such as nearly uniform smoothness and property ( P ) , are studied. Introduction. Orthogonal convexity has been introduced by A. Jimenez-Melado and E. Llorens-F'uster (see [3] and [4]) as a geome...

Let E be a rearrangement-invariant Banach function space on [0, 1], and let Γ(E) denote the set of all p ≥ 1 such that any sequence {xn} in E converging weakly to 0 has a subsequence {yn} with supm m−1/p‖ ∑ 1≤k≤m yn‖ < ∞. The set Γi(E) is defined similarly, but only sequences {xn} of independent random variables are taken into account. It is proved (under the assumption Γ(E) = {1}) that if Γi(E...

we introduce a new one-step iteration process to approximate common fixed points of twononexpansive mappings in banach spaces and prove weak convergence of the iterative sequence using (i)opial’s condition and (ii) kadec-klee property. strong convergence theorems are also established in banachspaces and uniformly convex banach spaces under the so-called condition ( a ), which is weaker thancom...