Recent reverses for the discrete generalised triangle inequality and its continuous version for vector-valued integrals in Banach spaces are surveyed. New results are also obtained. Particular instances of interest in Hilbert spaces and for complex numbers and functions are pointed out as well.

A d-contraction is a d-tuple (T1, . . . , Td) of mutually commuting operators acting on a common Hilbert space H such that ‖T1ξ1 + T2ξ2 + · · ·+ Tdξd‖ 2 ≤ ‖ξ1‖ 2 + ‖ξ2‖ 2 + · · ·+ ‖ξd‖ 2 for all ξ1, ξ2, . . . , ξd ∈ H. These are the higher dimensional counterparts of contractions. We show that many of the operator-theoretic aspects of function theory in the unit disk generalize to the unit ball...

Because of the limited capacity of coastal lands and conflicting interests among stakeholders for coastal resources, there are intensifying pressures to retain and provide more public access to the coast. Coastal gated communities have been developed increasingly in the middle shoreline of Caspian Sea in North of Iran. They are kind of exclusive space production as they restrict public access t...