The Stability Of Solution Maps For η-parameter Weak Vector Variational Inequality And The Existence And Uniqueness Of Fixed Point For Mixed Monotone Ternary Operators

In this paper, we introduce a new class of η-parameter weak vector variationalinequality in Banach space, which extends the existing parameter weak vector variationalinequality. The concepts ofη (y,x)function, invex set,η-hemicontinuous, η-stronglyC pseudomonotone mappings are introduced. We obtain new η-generalizedlinearization lemma. The stability of solution maps for η-parameter weak vectorvariational inequality are given by using this lemma. Finally, we present an example toverify our results.On the other hand, in this paper, partial order theory is used to study the fixed pointof a mixed monotone ternary operator A: P×P×Pâ†'P. The existence and uniquenessof a fixed point (A(u,u,u)=utype) are obtained without assuming the operators to becompact or continuous. In the end, the application to an integral equation is presented.Our results unify, generalize, and complement various known comparable results fromthe current literature.