where the constant factor [π/ sin(π/p)]p is also the best possible. Hardy-Hilbert inequalities are important in analysis and in their applications (see [7]). In recent years, many results (see [1, 3, 8–10]) have been obtained in the research of Hardy-Hilbert inequality. At present, because of the requirement of higher-dimensional harmonic analysis and higher-dimensional operator theory, multipl...

Some additive reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for complex-valued functions are provided as well.

Making use of the generalized hypergeometric functions, we introduce some generalized class of k−uniformly convex and starlike functions and for this class, we settle the Silverman’s conjecture for the integral means inequality. In particular, we obtain integral means inequalities for various classes of uniformly convex and uniformly starlike functions in the unit disc.

This article advances a communicative approach to social capital that views communication as the fundamental source of societal integration. We contend that integration occurring at the system level via news consumption and at the individual level via interpersonal discussion is amplified through ties at the community level. This cross-level interaction is theorized to encourage civic engagemen...