# GENERALIZED FUZZY RANDOM SET-VALUED MIXED VARIATIONAL INCLUSIONS INVOLVING RANDOM NONLINEAR ($A_\omega,\eta_\omega$)-ACCRETIVE MAPPINGS IN BANACH SPACES

Volume 3, Issue 1, pp 63-77 Publication Date: February 13, 2010
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### Authors

HONG GANG LI - Institute of Applied Mathematics Research, Chongqing University of Posts and TeleCommunications, Chongqing 400065, China.

### Abstract

The main purpose of this paper is to introduce and study a new class of random generalized fuzzy set-valued mixed variational inclusions involving random nonlinear ($A_\omega,\eta_\omega$)-accretive mappings in Banach Spaces. By using the random resolvent operator associated with random nonlinear ($A_\omega,\eta_\omega$)-accretive mappings, an existence theorem of solutions for this kind of random generalized fuzzy set-valued mixed variational inclusions is established and a new iterative algorithm with an random error is suggested and discussed. The results presented in this paper generalize, improve, and unify some recent results in this field.

### Keywords

• Generalized fuzzy random set-valued mixed variational inclusions
• random nonlinear ($A_\omega • \eta_\omega$)-accretive mappings
• random resolvent operator
• random fuzzy set-valued mapping
• convergence
• iterative algorithm with an random error.

•  49J40
•  47H06

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