## Approximation of a solution for a $$K$$-positive definite operator equation.(English)Zbl 0901.47002

An iterative method is constructed which converges strongly to the unique solution of the equation $$Ax=f$$ where $$A$$ is a $$K$$-positive definite operator on a domain of a real separable $$q$$-uniformly smooth Banach space, $$q>1$$. This class of Banach spaces includes the $$L_p$$ (or $$\ell_p$$) spaces for $$1<p<+\infty$$. The iterative process developed has been studied earlier for the case of Hilbert space. The result of the article is an extension of the similar result of C. E. Chidume and S. J. Aneke [Appl. Anal. 50, No. 3-4, 285-294 (1993; Zbl 0788.47051)] on the more general Banach spaces. Moreover, the weaker conditions were used instead of the commutativity assumption imposed in the mentioned article.

### MSC:

 47A50 Equations and inequalities involving linear operators, with vector unknowns

Zbl 0788.47051
Full Text:

### References:

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