The main result of this paper establishes that the known Arazy-Cwikel property holds for classes uniformly K-monotone spaces in quasi-Banach setting provided initial couple is mutually closed. As a consequence, we get class all K-spaces (i.e., interpolation which are described by real K-method) with respect to an arbitrary closed Banach enjoys property. Moreover, show also whenever couples invo...

Answering an old problem in nonlinear theory, we show that c0 cannot be coarsely or uniformly embedded into a reflexive Banach space, but that any stable metric space can be coarsely and uniformly embedded into a reflexive space. We also show that certain quasi-reflexive spaces (such as the James space) also cannot be coarsely embedded into a reflexive space and that the unit ball of these spac...

In this paper, we introduce a one-step iterative scheme for finding a common fixed point of a finite family of multivalued quasi-nonexpansive mappings in a real uniformly convex Banach space. We establish weak and strong convergence theorems of the propose iterative scheme under some appropriate conditions.

* Correspondence: [email protected]. edu.cn School of Computer and Information Engineering, Zhejiang Gongshang University, Hangzhou 310018, People’s Republic of China Full list of author information is available at the end of the article Abstract In this article, we introduce the concept of nonself uniformly quasi-Lipschitzian mapping and consider a new iterative scheme with errors to converge t...

We extend the recent results of R. Lata la and O. Guédon about equivalence of Lq-norms of logconcave random variables (KahaneKhinchin’s inequality) to the quasi-convex case. We construct examples of quasi-convex bodies Kn ⊂ IRn which demonstrate that this equivalence fails for uniformly distributed vector on Kn (recall that the uniformly distributed vector on a convex body is logconcave). Our e...

In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search step (gradient descent or Quasi-Newton iteration) into these uniformly optimal convex programming methods, and then enforce a monotone decreasing property of th...