'mutually influential' is correct and usable in written English.
You can use it to describe a relationship between two or more parties that is equally influential for each entity involved. For example, "The relationship between the teacher and student was mutually influential, each pushing the other to new heights of success."
The argument here is that such organizations experience a mutually influential and interactive effect in their strategy over time.
Deep processing and self-regulation also appeared to be mutually influential from year 2 to year 3.
Miller's most daring conceit, likening the mutually influential friendship between Tolkien and Lewis to that between Coleridge and Wordsworth, is persuasive.
Mutually influential and highly eclectic, they combined, especially in their drawings, the linear tensions of Italian Mannerism with bold contrasts of light and shade.
The defining characteristic of a Multidisciplinary Design Optimization (MDO) strategy or method, compared to the more traditional, sequential approach to conducting design work, is that the contributions of all mutually influential disciplines are concurrently taken into account.
The results show that, no matter in the extremities or in the whole bondline, the damage and stress evolutions are mutually influential processes, both of which are affected by the bondline thickness significantly.
He works on problems of the mutually-influential rise of professionalism and vernacular culture, the public reception of science, and the way in which fields of expertise are represented in popular media.
More recently, a number of MIT alumni have contributed influential, mutually supportive work on modality.
These aren't really mutually exclusive schools of thought — most influential Republicans will tell you they need to do both — but which approach you emphasize says a lot about what kind of Republican Party you would like to emerge from the ruins of Bushism.
According to the Belizean Grove's Web site, the group is a "constellation of influential women" who are building "long-term, mutually beneficial relationships".
At least one influential theory of poverty contends that the poor are too mutually dependent, and that this is one of their problems.
