This work presents a parametrized family of distances, namely the Alpha Procrustes on set symmetric, positive definite (SPD) matrices. The distances provide unified formulation encompassing both Bures-Wasserstein and Log-Euclidean between SPD We show that are Riemannian corresponding to metrics manifold matrices, which encompass Wasserstein metrics. is then generalized Hilbert-Schmidt operators...

Equilibrium problems have many uses in optimization theory and convex analysis and which is why different methods are presented for solving equilibrium problems in different spaces, such as Hilbert spaces and Banach spaces. The purpose of this paper is to provide a method for obtaining a solution to the equilibrium problem in Banach spaces. In fact, we consider a hybrid proximal point algorithm...