Characterizations of Möbius transformations by use of Apollonius points of some polygons

This theis consists of eight chapters. The first chapter is devoted to the introduction section. In the second chapter, some required preparatory notions recalled. In the third chapter, Möbius Transformations by Use of Apollonius Points of triangles were studied. In the chapters of fourth, fifth and sixth the characterizations of Möbius transformation are presented by use of Apollonius quadrilaterals, Apollonius pentagons and Apollonius hexagons, recpectively. In the seventh chapter, A Note on the Characteristics of Mobius Transformations are studied. In the final chapter, A New Characterization of Möbius Transformations by the Use of Apollonius Points of (2n − 1)-gons were examined.