We introduce a new concept of general $G$-$eta$-monotone operator generalizing the general $(H,eta)$-monotone operator cite{arvar2, arvar1}, general $H-$ monotone operator cite{xiahuang} in Banach spaces, and also generalizing $G$-$eta$-monotone operator cite{zhang}, $(A, eta)$-monotone operator cite{verma2}, $A$-monotone operator cite{verma0}, $(H, eta)$-monotone operator cite{fanghuang}...

Pruning techniques have recently been shown to speed up search algorithms by reducing the branching factor of large search spaces. One such technique is sleep sets, which were originally introduced as a pruning technique for model checking, and which have recently been investigated on a theoretical level for planning. In this paper, we propose a generalization of sleep sets and prove its correc...