Existence of fixed points for mixed monotone operators with perturbations and applications

Abstract

In this article we study a class of mixed monotone operators with perturbations and present some new tripled fixed point theorems by means of partial order theory,  we get the existence and
uniqueness of tripled fixed points without assuming the operator to
be compact or continuous, which extend the existing corresponding
results.  As applications, we utilize the results obtained in this
paper to study the existence and uniqueness of positive solutions
for a fractional differential equation boundary value problem.