Akyel, TuğbaÖrnek, Bülent Nafi2024-07-122024-07-122019978-0-7354-1930-80094-243X10.1063/1.51361232-s2.0-85076712220https://doi.org/10.1063/1.5136123https://hdl.handle.net/20.500.12415/74283rd International Conference of Mathematical Sciences (ICMS) -- SEP 04-08, 2019 -- Maltepe Univ, Istanbul, TURKEYWe consider the rigidity part of Schwarz Lemma. Let f be a holomorphic function in the unit disc D and vertical bar Rf(z)vertical bar < 1 for vertical bar z vertical bar < 1. We generalize the rigidity of holomorphic function and provide sufficient conditions on the local behaviour of f near a finite set of boundary points that needs f to be a finite Blaschke product. For a different version of the rigidity theorems of D. Burns-S.Krantz and D. Chelst, we present some more general results in which the bilogaritmic concave majorants are used. The strategy of these results relies on a special version of Phragmen-Lindelof princible and Harnack inequality.eninfo:eu-repo/semantics/openAccessHolomorphic FunctionBilogarithmic Concave MajorantHarnack InequalityPhragmen-Lindelof PrincibleConference ObjectN/A2183WOS:000505225800022N/A