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The phrase "a perception of mutual" is correct and usable in written English.
It can be used when discussing shared feelings, understandings, or viewpoints between two or more parties.
Example: "There is a perception of mutual respect between the two organizations, which has fostered a collaborative environment."
Alternatives: "a sense of shared" or "an understanding of reciprocity".
Exact(2)
The relationship between journalists and PRs is an intangible one, dependent on a perception of mutual advantage and respect for an unwritten code of ethics.
Others have stressed that the overall relationship between European corporate enterprises and the Indian and other Asian authorities was often an amicable one, based on a perception of mutual advantage, which often led to an increase in trade and regional prosperity.
Similar(58)
It is a limited partnership sustained by the perception of mutual if asymmetrical gains, and the wisdom to underplay significant differences where they occur.
Hence, Ganesan (1994) defined long-term relationship orientation as the perception of mutual dependence that joint relationship outcomes are related to future rewards.
"There's a perception of professionalism".
(a) Perception of a single photon.
The result is a perception of movement.
This creates a perception of scarcity.
Among all management decisions, structural downsizing has the biggest impact on employees, because it breaks the psychological contract – defined by organizational researcher Denise Rousseau as an unwritten set of mutual beliefs, perceptions, and informal obligations between employer and employee.
It is a system of mutual dependency.
A relationship of mutual respect.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com