The Schwarz lemma stands as a cornerstone result in complex analysis, constraining holomorphic self-mappings of the unit disc by bounding both their magnitude and derivative. Traditionally, it affirms ...

In this paper we discuss holomorphic mappings f of the unit disc 𝕌 and corresponding index defined as I f ( z )= zf'( z ) f( z ) . We are interested in finding bounds on the growth of functions f and ...

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