Harmonik yalınkat fonksiyonlar

Abstract

Harmonic functions are complex valued functions which do not need to be analytic. The theory of harmonic univalent functions is one of the most popular branches of complex analysis. In this thesis we first survey standard topics in the theory of univalent functions, and harmonic univalent functions, and then describe the tools which will be used in the sequel. By using harmonic univalent functions and univalent functions simultaneously, we define a new class of harmonic univalent functions and obtain the growth theorem, the distortion theorem, the Heinz inequality, the coefficient inequality and boundaries of Jacobian for this new class. Also we obtain a new coefficient inequality for the second coefficients of analytic and co-analytic parts of harmonic univalent functions.