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International Journal of Mathematics and Mathematical Sciences
Volume 17, Issue 2, Pages 389-396
http://dx.doi.org/10.1155/S0161171294000530

On the existence and uniqueness problems of solutions for set-valued and single-valued nonlinear operator equations in probabilistic normed spaces

1Department of Mathematics, Sichuan University, Sichuan, Chengdu 610064, China
2Department of Mathematics, Gyeongsang National University, Jinju 660-701, Korea
3Jiangsu Industrial and Commercial School, Jiangsu, Nantong 226004, China

Received 11 February 1992; Revised 22 October 1992

Copyright © 1994 Hindawi Publishing Corporation. 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.

Abstract

In this paper, we introduce the concept of more general probabilistic contractors in probabilistic normed spaces and show the existence and uniqueness of solutions for set-valued and single-valued nonlinear operator equations in Menger probabilistic normed spaces.