Inheritance Kulkarni - Nomizu product in generalized BK-fifth recurrent Finsler space by Lie - derivative

This paper deals with space known as "generalized fifth recurrent Finsler space." The core idea centers around a mathematical object called the" Inheritance Kulkarni-Nomizu product" which is applied to two Ricci tensors satisfy an inheritance property. We apply the inheritance property with Kulkarni - Nomizu product of two Ricci tensosrs by using Lie - derivative in generalized fifth recurrent Finsler space. In addition, we prove that the Lie - derivative of the inheritance Kulkarni - Nomizu product of K-Ricci tensor and H-Ricci tensor vanishes simultaneously.