On the order of starlikeness and convexity of complex harmonic functions with a two-parameter coefficient condition

The article of J. Clunie and T. Sheil-Small [3], published in 1984, intensified the investigations of complex functions harmonic in the unit disc \(\Delta\). In particular, many papers about some classes of complex mappings with the coefficient conditions have been published. Consideration of this type was undertaken in the period 1998–2004 by Y. Avci and E. Złotkiewicz [2], A. Ganczar [5], Z. J. Jakubowski, G. Adamczyk, A. Łazinska and A. Sibelska [1], [8], [7], H. Silverman [12] and J. M. Jahangiri [6], among others. This work continues the investigations described in [7]. Our results relate primarily to the order of starlikeness and convexity of functions of the aforementionedclasses.