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The purpose of this paper is to introduce and study the notion of generalizedReynolds operators on Lie triple systems with representations (Abbr.\textsf{L.t.sRep} pairs) as generalization of weighted Reynolds operators onLie triple systems. First, We construct an $L_{\infty}$-algebra whoseMaurer-Cartan elements are generalized Reynolds operators. This allows us todefine a Yamaguti cohomology of a generalized Reynolds operator. Thiscohomology can be seen as the Yamaguti cohomology of a certain Lie triplesystem with coefficients in a suitable representation. Next, we studydeformations of generalized Reynolds operators from cohomological points ofview and we investigate the obstruction class of an extendable deformation oforder $n$. We end this paper by introducing a new algebraic structure, inconnection with generalized Reynolds operator, called NS-Lie triple system.Moreover, we show that NS-Lie triple systems can be derived from NS-Liealgebras.

Maurer-Cartan type cohomology on generalized Reynolds operators and NS-structures on Lie triple systems