___

• [1] Aczél, J. and McKiernan, M.A., On the characterization of plane projective and complex Möbius transformations. Math. Nachr. 33, (1967), 315–337.
• [2] Beardon, A.F. and Minda, D., Sphere-preserving maps in inversive geometry. Proc. Amer. Math. Soc. 130 (2002), no. 4, 987–998.
• [3] Beardon, A.F., The geometry of discrete groups, Springer-Verlag, New York, 1983.
• [4] Carathéodory, C., The most general transformations of plane regions which transform circles into circles. Bull. Am. Math. Soc. 43, (1937), 573–579.
• [5] Demirel, O. and Seyrantepe, E.S., A characterization of Möbius transformations by use of hyperbolic regular polygons. J. Math. Anal. Appl. 374 (2011), no. 2, 566–572.
• [6] Demirel, O., A characterization of Möbius transformations by use of hyperbolic regular star polygons. Proc. Rom. Acad. Ser. A Math. Phys. Tech. Sci. Inf. Sci. 14 (2013), no. 1, 13–19.
• [7] Demirel, O., Degenerate Lambert quadrilaterals and Möbius transformations. Bull. Math. Soc. Sci. Math. Roumanie, (accepted for publication).
• [8] Haruki, H and Rassias, T.M., A new characteristic of Möbius transformations by use of Apollonius quadrilaterals. Proc. Amer. Math. Soc. 126 (1998), no. 10, 2857–2861.
• [9] Höfer, R., A characterization of Möbius transformations. Proc. Amer. Math. Soc. 128 (2000), no. 4, 1197–1201.
• [10] Jing, L., A new characteristic of Möbius transformations by use of polygons having type A. J. Math. Anal. Appl. 324 (2006), no. 1, 281–284.
• [11] Jones, G.A and Singerman, D., Complex functions. An algebraic and geometric viewpoint. Cambridge University Press, Cambridge, 1987.
• [12] Ungar, A.A., Analytic hyperbolic geometry. Mathematical foundations and applications. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005
• [13] Ungar, A.A., The hyperbolic square and Möbius transformations, Banach J. Math. Anal. 1 (2007), no. 1, 101–116.
• [14] Yang, S. and Fang, A., A new characteristic of Möbius transformations in hyperbolic geometry. J. Math. Anal. Appl. 319 (2006), no. 2, 660–664.
• [15] Yang, S. and Fang, A., Corrigendum to "A new characteristic of Möbius transformations in hyperbolic geometry, J. Math. Anal. Appl. 319 (2) (2006) 660-664" J. Math. Anal. Appl. 376 (2011), no. 1, 383–384.