Recently, Takahashi has introduced the James and von Neumann-Jordan type constants. In this paper, we present some sufficient conditions for uniform normal structure and therefore the fixed point property of a Banach space in terms of the James and von Neumann-Jordan type constants and the Ptolemy constant. Our main results of the paper significantly generalize and improve many known results in...

Correspondence: zuozhanfei@139. com Department of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404000, China Abstract We determine and estimate the Ptolemy constant of absolute normalized norms on R by means of their corresponding continuous convex functions on [0, 1]. Moreover, the exact values were calculated in some concrete Banach spaces. 2000 Mathematics Subject C...

Correspondence: zuozhanfei@139. com Department of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404000, China Abstract We determine and estimate the Ptolemy constant of absolute normalized norms on R by means of their corresponding continuous convex functions on [0, 1]. Moreover, the exact values were calculated in some concrete Banach spaces. 2000 Mathematics Subject C...

This paper shows how Ptolemy II discrete-event (DE) models can be formally analyzed using Real-Time Maude. We formalize in RealTime Maude the semantics of a subset of hierarchical Ptolemy II DE models, and explain how the code generation infrastructure of Ptolemy II has been used to automatically synthesize a Real-Time Maude verification model from a Ptolemy II design model. This enables a mode...

This paper defines a real-time rewriting logic semantics for a significant subset of Ptolemy II discreteevent models. This is a challenging task, since such models combine a synchronous fixed-point semantics with hierarchical structure, explicit time, and a rich expression language. The code generation features of Ptolemy II have been leveraged to automatically synthesize a Real-Time Maude veri...

We provide examples of non-locally compact geodesic Ptolemy metric spaces which are not uniquely geodesic. On the other hand, we show that locally compact, geodesic Ptolemy metric spaces are uniquely geodesic. Moreover, we prove that a metric space is CAT(0) if and only if it is Busemann convex and Ptolemy.