We investigate what we call a conformal ℎ-vector-change in Finsler spaces, namelywhere, is a function of only, and ( , ): = ( , ) , where ≔ ( , ) is an ℎ-vector. This change generalizes various types of changes: conformal changes, generalized Randers changes, Randers change. Under this change, we obtain the relationships between some tensors associated with ( , ) and the corresponding tensors associated with( , ̅ ). Next, we express the conditions for more generalized -th root metrics ̃1 = √ 1 2 1 + 1 + 1 and ̃2 = √ 2 2 2 + 2 + 2 , when is established conformal ℎ-vector-change and 1 , 2 are even numbers and other case 1 , 2 even and odd numbers, respectively. Finally, we prove that under these conditions conformal ℎ-vector-change in Finsler spaces reduces to conformal -change in Finsler spaces.

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The purpose of the present paper is devoted to studying the conditions for more generalized m-th root metricswhen is established generalized Randers change and m 1 , m 2 are odd numbers. As well as, we give the condition for the case of m 1 , m 2 are even and odd numbers, respectively. Finally, we prove that under these conditions generalized Randers metric reduces to Randers metric.