Total Convexity for Powers of the Norm in Uniformly Convex Banach Spaces
Dan Butnariu, Alfredo Noel Iusem, Elena Resmerita · Journal of convex analysis · 2000
The aim of the paper is to show that, in uniformly convex Banach spaces, the powers of the norm with exponent r > 1 share a property called total convexity. Using this fact we establish a formula for determining Bregman projections on closed hyperplanes and half spaces. This leads to a method for solving linear operator equations (e.g., first order Fredholm and Volterra equations) in spaces which are uniformly convex and smooth.