International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 1, Pages 111-118

Nonlinear random operator equations and inequalities in Banach spaces

Antonios Karamolegos and Dimitrios Kravvaritis

Department of Mathematics, National Technical University of Athens, Zografou Campus, Athens 157 73, Greece

Received 31 July 1989; Revised 5 May 1990

Copyright © 1992 Antonios Karamolegos and Dimitrios Kravvaritis. 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.


In this paper we give some new existence theorems for nonlinear random equations and inequalities involving operators of monotone type in Banach spaces. A random Hammerstein integral equation is also studied. In order to obtain random solutions we use some results from the existing deterministic theory as well as from the theory of measurable multifunctions and, in particular, the measurable selection theorems of Kuratowski/Ryll-Nardzewski and of Saint-Beuve.