Existence and uniqueness of $\xi\eta$-multiple fixed points of mixed monotone operators

Neeraj Anant Pande, J. Achari

In this paper, we firstly coin the concept of $\xi\eta$-multiple fixed point and then obtain necessary and sufficient conditions for a class of mixed monotone operators to have this point. We see that these conditions can be considerably loosened for monotone operators acting on pairs of points, which are multiples of the same point. Also when a cone is chosen to be a normal solid cone and monotone operator on interior of the cone, the necessary and sufficient conditions get reduced further. The introduction of adjoint sequence generalizes further the main result.