On Banach Contraction Principle for Generalized Fuzzy Variational Inequality Problems

The main objective of the paper is to study the existence theorem of the newly defined generalized fuzzy ψ-variational inequality problem, generalized fuzzy ψ-complementarity problem. Uniqueness of the problems are also studied. Existence of these problems are established with the help of unique point condition of η. The existence of the solution of generalized fuzzy ψ-variational inequality problems is studied with the help of Banach contraction principle. The existence of the solution of generalized fuzzy ψ-complementarity problem is established in η-invex space.Conclusion: Equality of the solution sets of generalized fuzzy ψ-variational inequality problem and generalized fuzzy ψ-complementarity problem is shown using unique point condition of the bifunction η. Unique of the solution of generalized fuzzy ψ-variational inequality problem and generalized fuzzy ψ-complementarity problem is studied using strictly monotonicity condition. Existence theorems of the solution of generalized fuzzy ψ-variational inequality problem are shown using Banach contraction principle in the presence of Lipschitz continuous, strongly monotone mappings T_ψ and weakly monotonicity of η. Existence theorems of the solution of generalized fuzzy ψ-complementarity problem in the presence of condition C_0.