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For every linear operator between inner product spaces whose operator norm is less than or equal to one, we show that the restriction to the Möbius gyrovector space is Lipschitz continuous with respect to the Poincaré metric. Moreover, the Lipschitz constant is precisely the operator norm. [ABSTRACT FROM AUTHOR]

We show some Cauchy–Bunyakovsky–Schwarz type inequalities related to the Möbius operations in complex inner product spaces which are extensions of a similar type inequality obtained recently, and we discuss some properties. [ABSTRACT FROM AUTHOR]

In this article, we show two fundamental features of the restriction of Möbius operations to the real numbers, that is, a Cauchy type inequality and a criterion for convergence of series. [ABSTRACT FROM AUTHOR]