On Several Bounds for Types of Angular Distances

Abstract

In this study, we introduce the expression dλ(x,y):=λ∥x∥+(1−λ)∥y∥−∥λx+(1−λ)y∥ on the real normed space X(X,∥·∥), where x,y∈X and λ∈R. We characterize this expression and find various estimates of it. We also obtain a generalization and some refinements of Maligranda’s inequality. Finally, we give some relations between dλ(x,y) and several types of angular distances between two nonzero vectors in a real normed space.