  The purpose of the present paper is to investigate cohomologies of Reynolds
Lie-Yamaguti algebras of any weight and provide some applications. First, we
introduce the notion of Reynolds Lie-Yamaguti algebras and give some new
examples. Moreover, cohomologies of Reynolds operators and Reynolds
Lie-Yamaguti algebras with coefficients in a suitable representation are
established. Finally, formal deformations and abelian extensions of Reynolds
Lie-Yamaguti algebras are characterized in terms of lower degree cohomology
groups.
