Total Convexity for Powers of the Norm in Uniformly Convex Banach Spaces
Copyright policy )Total Convexity for Powers of the Norm in Uniformly Convex Banach Spaces
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.
- University of Haifa Israel
linear operator equations, Geometry and structure of normed linear spaces, uniformly convex Banach spaces, Bregman projections, first order Fredholm and Volterra equations, total convexity, Equations and inequalities involving linear operators, with vector unknowns
linear operator equations, Geometry and structure of normed linear spaces, uniformly convex Banach spaces, Bregman projections, first order Fredholm and Volterra equations, total convexity, Equations and inequalities involving linear operators, with vector unknowns
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