Abstract
In this paper, we study an operator version of the modified Browder-Tikhonov regularization method for finding a common solution for a system of ill-posed operator equations involving m-accretive operators Ai, i =0 , ... , N, in a reflexive Banach space. The convergence rates of the regularized solutions are estimated not only in the infinite-dimensional space, but also in connection with its finite-dimensional approximations without the weakly sequential continuity of the dual mapping. MSC: 47H17; 47H20
Highlights
Let X be a real reflexive Banach space with the property of approximations and its dual space X∗ be strictly convex
Our problem is to find a common solution of the following operator equations: Ai(x) = fi, fi ∈ R(Ai), i =, . . . , N
We show that a common solution of ( . ) involving m-accretive operators Ai, without the weakly sequentially continuous property of j, can be approximated by the modified Browder-Tikhonov regularization method which is described by the following operator equation: N
Summary
Let X be a real reflexive Banach space with the property of approximations and its dual space X∗ be strictly convex. Our problem is to find a common solution of the following operator equations: Ai(x) = fi, fi ∈ R(Ai), i = , . For m-accretive operators, some results of the approximating solution for each equation in
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