Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces.

*(English)*Zbl 1130.47046Summary: The aim of this paper is twofold. First, several basic mathematical concepts involved in the construction and study of Bregman type iterative algorithms are presented from a unified analytic perspective. Also, some gaps in the current knowledge about those concepts are filled in. Second, we employ existing results on total convexity, sequential consistency, uniform convexity and relative projections in order to define and study the convergence of a new Bregman type iterative method of solving operator equations.

##### MSC:

47J25 | Iterative procedures involving nonlinear operators |

46B20 | Geometry and structure of normed linear spaces |

49J53 | Set-valued and variational analysis |

90C25 | Convex programming |

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