Article ID: | iaor2014271 |
Volume: | 7 |
Issue: | 8 |
Start Page Number: | 1929 |
End Page Number: | 1955 |
Publication Date: | Dec 2013 |
Journal: | Optimization Letters |
Authors: | Cho Yeol, Balooee Javad |
Keywords: | inequality problems, Lipschitz functions, fixed point theory |
In this paper, we introduce and study a new class of extended general nonlinear mixed variational inequalities and a new class of extended general resolvent equations and establish the equivalence between the extended general nonlinear mixed variational inequalities and implicit fixed point problems as well as the extended general resolvent equations. Then by using this equivalent formulation, we discuss the existence and uniqueness of solution of the problem of extended general nonlinear mixed variational inequalities. Applying the aforesaid equivalent alternative formulation and a nearly uniformly Lipschitzian mapping