关键词: N. A. Menger PN-space, (Φ, Δ)-probabilistic contractor couple, selective operator, nonlinear operator equations

Abstract: The concept of (Ф, Δ)-type probabilistic contractor couple was introduced which simplifies and weakens the definition of probabilistic contractor couple given by Zhang Shisheng. The existence and uniqueness of the solutions for a system of nonlinear operator equations with this kind of propabilistic contractor couple in N.A. Menger PN-spaces were studied. The works improve and extend the corresponding results by M. Altman, A.C.Lee,W.J. Padgett et al.

Key words: N. A. Menger PN-space, (Φ, Δ)-probabilistic contractor couple, selective operator, nonlinear operator equations