## Approximation of a solution for a $$K$$-positive definite operator equation in uniformly smooth separable Banach spaces.(English)Zbl 0946.47007

For a linear equation with a $$K$$-positive definite operator over a separable uniformly smooth Banach space a new iteration method is constructed which converges strongly to a unique solution. This extends a result of C. E. Chidume and M. O. Osilike [J. Math. Anal. Appl. 210, No. 1, 1-7 (1997; Zbl 0901.47002)].

### MSC:

 47A50 Equations and inequalities involving linear operators, with vector unknowns 47B48 Linear operators on Banach algebras 41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)

Zbl 0901.47002
Full Text:

### References:

 [1] Chidume, C.E.; Aneke, S.J., Existence, uniqueness and approximation of a solution for a K-positive definite operator equation, Appl. anal., 50, 285-294, (1993) · Zbl 0788.47051 [2] Chidume, C.E.; Osilike, M.O., Approximation of a solution for a K-positive definite operator equation, J. math. anal. appl., 210, 1-7, (1997) · Zbl 0901.47002 [3] Petryshyn, W.V., Direct and iterative methods for the solution of linear operator equations in Hilbert spaces, Trans. amer. math. soc., 105, 136-175, (1962) · Zbl 0106.09301 [4] Reich, S., An iterative procedure for constructing zeros of accretive sets in Banach spaces, Nonlinear anal., 2, 85-92, (1978) · Zbl 0375.47032 [5] Wang, X.L., Fixed point iteration for local strictly pseudo-contractive mapping, Proc. amer. math. soc., 113, 727-731, (1991) · Zbl 0734.47042
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.