title: Sequence spaces [Formula: see text] and [Formula: see text] with application in clustering.
abstract: Distance measures play a central role in evolving the clustering technique. Due to the rich mathematical background and natural implementation of [Formula: see text] distance measures, researchers were motivated to use them in almost every clustering process. Beside [Formula: see text] distance measures, there exist several distance measures. Sargent introduced a special type of distance measures [Formula: see text] and [Formula: see text] which is closely related to [Formula: see text]. In this paper, we generalized the Sargent sequence spaces through introduction of [Formula: see text] and [Formula: see text] sequence spaces. Moreover, it is shown that both spaces areBK-spaces, and one is a dual of another. Further, we have clustered the two-moon dataset by using an induced [Formula: see text]-distance measure (induced by the Sargent sequence space [Formula: see text]) in the k-means clustering algorithm. The clustering result established the efficacy of replacing the Euclidean distance measure by the [Formula: see text]-distance measure in the k-means algorithm.
authors.affiliation: Department of Mathematics, South Asian University, New Delhi, India.
authors.forename: Mohd Shoaib
authors.initials: MS
authors.lastname: Khan
authors.affiliation: Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589 Saudi Arabia.
authors.forename: Badriah As
authors.initials: BA
authors.lastname: Alamri
authors.affiliation: Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589 Saudi Arabia.|Department of Mathematics, Aligarh Muslim University, Aligarh, 202002 India.
authors.forename: M
authors.initials: M
authors.lastname: Mursaleen
authors.affiliation: Department of Mathematics, South Asian University, New Delhi, India.
authors.forename: Qm Danish
authors.initials: QD
authors.lastname: Lohani
keywords: clustering; double sequence; k-means clustering; two-moon dataset