  In this paper, we introduce the concept of uniformly bounded fibred coarse
embeddability of metric spaces, generalizing the notion of fibred coarse
embeddability defined by X. Chen, Q. Wang and G. Yu. Moreover, we show its
relationship with uniformly bounded a-T-menability of groups. Finally, we give
some examples to illustrate the differences between uniformly bounded fibred
coarse embeddability and fibred coarse embeddability.
