Random Directional Contractors and Their Applications

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Ding Xie-ping. Random Directional Contractors and Their Applications[J]. Applied Mathematics and Mechanics, 1986, 7(12): 1107-1120.

Citation:

Ding Xie-ping. Random Directional Contractors and Their Applications[J]. Applied Mathematics and Mechanics, 1986, 7(12): 1107-1120.

Citation:

Ding Xie-ping. Random Directional Contractors and Their Applications[J]. Applied Mathematics and Mechanics, 1986, 7(12): 1107-1120.

Abstract

In this paper, as the generalizations of Altman's directional contractors^[4,5] and Lee and Padgett's random contractors^[1,2] we introduce the concept of random directional contractors for set-valued random operators. Using the new concept and transfinite induction, we show several existence theorems to solutions of nonlinear set-valued random operator equations. Our theorems improve and generalize the corresponding results in [1,2,4,5,11]. Next, some applications of our results to nonlinear random integral and differential equations are given.

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