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Journal of Convex Analysis, Vol. 07, No. 2, pp. 319-334 (2000)
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Total Convexity for Powers of the Norm in Uniformly Convex Banach Spaces

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Butnariu, Dan; Iusem, Alfredo N.; Resmerita, Elena

Dept. of Mathematics University of Haifa 31905 Haifa Israel

Inst. de Matématica Pura e Aplicada Estrada Dońa Castorina 110 Rio de Janeiro, R.J., CEP 22460-320 Brazil

Dept. of Mathematics University of Haifa 31905 Haifa Israel

**Abstract:** 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.

**Full text of the article:**

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