On a system of extended general variational inclusions

Abstract

At the present paper, a new system of extended general nonlinear variational inclusions is introduced and using the resolvent operator technique, equivalence between the aforesaid system and the fixed point problem is verified. By using this alternative equivalent formulation, the existence and uniqueness theorem for solution of the system of extended general nonlinear variational inclusions is demonstrated and two new iterative schemes for solving this system of extended general nonlinear variational inclusions are suggested and analyzed. The convergence analysis of the proposed iterative methods under some suitable conditions is studied. Some errors in a recent article by Noor et al. (J Inequal Appl 2011:10, 2011) are found and the incorrectness of the results of the cited paper is proved. Also, the results of the aforementioned paper are revised and corrected.