ON STARLIKE HARMONIC FUNCTIONS

Year 2019, Volume: 9 Issue: 4, 704 - 711, 01.12.2019

S. NOSRATİ A. ZİREH

Abstract

Uniformly starlike univalent functions introduced by Goodman and we develop this idea over harmonic functions. We introduce a subclass of harmonic univalent functions which are fully starlike and uniformly starlike also. In the following we will mention some examples of this subclass and obtain two necessary and sucient conditions, one with the inequality form and other with convolution.

Keywords

Uniformly starlike function, Fully-Starlike function, Harmonic function, Convolution.

References

• Ahuja Om P., (2005) Planar harmonic univalent and related mappings, J. Inequal. Pure Appl. Math. 6 (4), Art-122.
• Chuaqui M., Duren P. and Osgood B., (2004), Curvature properties of planar harmonic mappings, Comput. Methods Funct. Theory 4 (1), 127-142.
• Clunie J. and Sheil-Small T., (1984), Harmonic Univalent Functions, Ann. Acad. Sci. Fenn. Ser. A. I. Math. 9 (2), pp. 3-25.
• Duren P. L., (2004) Harmonic Mappings in the Plane, Cambridge University Press, New York.
• Goodman A. W., (1991), On Uniformly Starlike Functions, J. Math. Ana. & App. 155, pp. 364-370.
• Mocanu P. T., (1980), Starlikeness and convexity for nonanalytic functions in the unit disc, Mathe- matica (Cluj), 22, (45), pp. 77-83.
• Nezhmetdinov I. R., (1997), Classes of Uniformly Convex and Uniformly Starlike Functions as Dual Sets, J. Math. Anal. Appl., 216, pp. 40-47.
• Pommerenke Ch., (1975), Univalent Functions, Vandenhoeck and Ruprecht, G¨ottingen.
• Yasar, E. and Yalcin, S., (2012), On Sakaguchi-type harmonic univalent functions, Int. J. Open Probl. Complex Anal. 4, (3), pp. 7-14.
• Yasar, E. and Yalcin, S., (2014), Coefficient inequalities for certain classes of Sakaguchi-type harmonicfunctions, Southeast Asian Bull. Math. 38, (6), pp. 925-931.