Distance measures play a central role in evolving the clustering technique. Due to the rich mathematical background and natural implementation of distance measures, researchers were motivated to use them in almost every clustering process. Beside distance measures, there exist several distance measures. Sargent introduced a special type of distance measures and which is closely related to . In this paper, we generalized the Sargent sequence spaces through introduction of and sequence spaces. Moreover, it is shown that both spaces are BK-spaces, and one is a dual of another. Further, we have clustered the two-moon dataset by using an induced -distance measure (induced by the Sargent sequence space ) in the k-means clustering algorithm. The clustering result established the efficacy of replacing the Euclidean distance measure by the -distance measure in the k-means algorithm.

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