In this article, we considered bidual spaces and reflexivity of real normed spaces. At first we proved some corollaries applying Hahn-Banach theorem and showed related theorems. In the second section, we proved the norm of dual spaces and defined the natural mapping, from real normed spaces to bidual spaces. We also proved some properties of this mapping. Next, we defined real normed space of R...

Given a normed cone (X , p) and a subcone Y, we construct and study the quotient normed cone (X/Y, p̃) generated by Y . In particular we characterize the bicompleteness of (X/Y, p̃) in terms of the bicompleteness of (X , p), and prove that the dual quotient cone ((X/Y )∗,‖ · ‖p̃,u) can be identified as a distinguished subcone of the dual cone (X∗,‖ · ‖p,u). Furthermore, some parts of the theory ar...

In this paper we use the tableau as a means to prove decidability of weak bisimulation for normed BPA. Decidability was proved for a restricted subclass, the totally normed processes by Hirshfeld [9]. However in the case that weak bisimilarity to be decidable is inequivalence is finitely approximable. In this paper we relax restriction of totally normedness and prove decidability of weak bisimi...

Based on the analysis of stratification structure on random normed modules, we first present the notion of random smoothness in random normed modules. Then, we establish the relations between random smoothness and random strict convexity. Finally, a type of Gâteaux differentiability is defined for random norms, and its relation to random smoothness is given. The results are helpful in the furth...

We present a polynomial-time algorithm deciding bisimilarity between a normed BPA process and a normed BPP process. This improves the previously known exponential upper bound by Černá, Křet́ınský, Kučera (1999). The algorithm relies on a polynomial bound for the “finite-state core” of the transition system generated by the BPP process. The bound is derived from the “prime form” of the underlying...

It is shown that every fuzzy n-normed space naturally induces a locally convex topology, and that every finite dimensional fuzzy n-normed space is complete.

Extending results of Hershberger and Suri for the Euclidean plane, we show that ball hulls and ball intersections of sets of n points in strictly convex normed planes can be constructed in O(n log n) time. In addition, we confirm that, like in the Euclidean subcase, the 2-center problem with constrained circles can be solved also for strictly convex normed planes in O(n2) time. Some ideas for e...

A process ∆ is regular if it is bisimilar to a process ∆′ with finitely many states. We prove that regularity of normed PA processes is decidable and we present a practically usable polynomial-time algorithm. Moreover, if the tested normed PA process ∆ is regular then the process ∆′ can be effectively constructed. It implies decidability of bisimulation equivalence for any pair of processes suc...