Uniform Convexity and Bishop-Phelps-BollobÃ¡s Property A new characterization of the uniform convexity of Banach space is obtained in the sense of Bishop-Phelps-BollobÃ¡s theorem. It is also proved that the couple of Banach spaces $(X,Y)$ has the bishop-phelps-bollobÃ¡s property for every banach space $y$ when $X$ is uniformly convex. As a corollary, we show that the Bishop-Phelps-BollobÃ¡s theorem holds for bilinear forms on $\ell_p\times \ell_q$ ($1\lt p, q\lt \infty$). Keywords:Bishop-Phelps-BollobÃ¡s property, Bishop-Phelps-BollobÃ¡s theorem, norm attaining, uniformly convexCategories:46B20, 46B22