On Partial Sums of Regular Functions | ||
| Al-Mustansiriyah Journal of Science | ||
| Article 1, Volume 27, Issue 2, April 2016, Pages 105-110 | ||
| Author | ||
| Shatha S. Alhily | ||
| Abstract | ||
| Let f(z)be regular in the unit disk D (|z|<1) then each of its partial sums will have the same properties of function. For instance, if f(z) be univalent in D, then each of its partial sums be univalent in the disk D_(1⁄4)={z∈D;|z|<1/4}(cf.[12]). The purpose of this paper on the contrary to what the above, through putting a sharp condition on the partial sum of f(z), that will make f(z) belong to the certain class in theory of complex functions such as , a univalent function , p-valent function, p-valent function has p zeros at the origin in the unit disk , and p-valent and regular function in the punctured unit disk │ζ│>1 except for a pole at ζ=∞, which have been addressed in this paper. | ||
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