Journal of Applied Mathematics and Stochastic Analysis
Volume 10 (1997), Issue 1, Pages 47-55

Stochastic approximation-solvability of linear random equations involving numerical ranges

Ram U. Verma1,2

1International Publications, 12046 Coed Drive, Orlando 32826 , Florida, USA
2Istituto per la Ricerca di Base, Division of Mathematics, Monteroduni (IS), Molise, I-86075, Italy

Received 1 September 1995; Revised 1 February 1996

Copyright © 1997 Ram U. Verma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The random (or stochastic) approximation-solvability, based on a projection scheme, of linear random operator equations involving the theory of the numerical range of a bounded linear random operator is considered. The obtained results generalize results with regard to the deterministic approximation-solvability of linear operator equations using the Galerkin convergence method.