Brief communications

Regularization of operator equations with $B$-symmetric and $B$-positive operators in Banach spaces

P. A. Chistyakov

Chair of Computational Mathematics, Ural State University, Ekaterinburg, Russia

Abstract: In this paper we consider a family of regularization methods for linear operator equations with $B$-symmetric and $B$-positive operators. We establish convergence theorems for regularized solutions and their discrete approximations.

Keywords: $B$-symmetric operator, $B$-positive operator, uniformly convex space, Efimov–Stechkin space, discretization, iterative process, subgradient, subdifferential.

UDC: 517.983+517.988

Received: 04.02.2009

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2009, 53:10, 72–77

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