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Publication Embargo Harmonic mappings for which second dilatation is Janowski functions(2013) Yavuz Duman, Emel; Kahramaner, Yasemin; Darus, Maslina; POLATOĞLU, YAŞAR; 111202; 199370; 8366In the present paper we extend the fundamental property that if h(z) and g(z) are regular functions in the open unit disc D with the properties h(0) = g(0) = 0, h maps D onto many-sheeted region which is starlike with respect to the origin, and Re g ′ (z) h′(z) > 0, then Re g(z) h(z) > 0, introduced by R.J. Libera [5] to the Janowski functions and give some applications of this to the harmonic functions.Publication Embargo Harmonic Function For Which The Second Dilatation is Alpha-Spiral(Springer International Publishing Ag, Gewerbestrasse 11, Cham, Ch-6330, Switzerland, 2012) Duman Yavuz, Emel; Aydoğan, Melike; Kahramaner, Yasemin; POLATOĞLU, YAŞAR; 111202; 35549; 199370; 8366Let f = h + (g) over bar be a harmonic function in the unit disc . We will give some properties of f under the condition the second dilatation is alpha-spiralPublication Embargo Harmonic mappinggs for which co-analytic part is a close-to-convex function of order b(2015) Kahramaner, Yasemin; Aydoğan, Seher Melike; POLATOĞLU, YAŞAR; 199370; 8366; 35549In the present paper we investigate a class of harmonic mappings for which the second dilatation is a close-to-convex function of complex order b, b ∈ C/{0} (Lashin in Indian J. Pure Appl. Math. 34(7):1101-1108, 2003).Publication Metadata only Quasiconformal Harmonic Mappings Related to Janowski Starlike Functions(Univ Kebangsaan Malaysia, Faculty Science & Technology, Bangi, Selangor, 43600, Malaysia, 2014-12) Kahramaner, Yasemin; POLATOĞLU, YAŞAR; 8366; 199370Let f(z) = h(z) + <(g(z))over bar> be a univalent sense-preserving harmonic mapping of the open unit disc D = {z vertical bar vertical bar z vertical bar < 1}. If f satisfies the condition vertical bar omega(z)vertical bar= vertical bar g'(z)/h'(z)vertical bar< k, 0 < k < 1, then is called k-quasiconformal harmonic mapping in D. The main purpose of this paper was to give some properties of the class of k-quasiconformal mappings related to Janowski starlike functions.