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R. Wilson, Determinantal criteria for meromorphic functions. Proc. Lond. Math. Soc. 4, 357-374 (1954).

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Article

Upper Bound of Partial Sums Determined by Matrix Theory

1Institute of Mathematical Sciences, University Malaya, Malaysia,


Turkish Journal of Analysis and Number Theory. 2015, Vol. 3 No. 6, 149-153
DOI: 10.12691/tjant-3-6-2
Copyright © 2015 Science and Education Publishing

Cite this paper:
Rabha W. Ibrahim. Upper Bound of Partial Sums Determined by Matrix Theory. Turkish Journal of Analysis and Number Theory. 2015; 3(6):149-153. doi: 10.12691/tjant-3-6-2.

Correspondence to: Rabha  W. Ibrahim, Institute of Mathematical Sciences, University Malaya, Malaysia,. Email: rabhaibrahim@yahoo.com

Abstract

One of the major problems in the geometric function theory is the coefficients bound for functional and partial sums. The important method, for this purpose, is the Hankel matrix. Our aim is to introduce a new method to determine the coefficients bound, based on the matrix theory. We utilize various kinds of matrices, such as Hilbert, Hurwitz and Turan. We illustrate new classes of analytic function in the unit disk, depending on the coefficients of a particular type of partial sums. This method shows the effectiveness of the new classes. Our results are applied to the well known classes such as starlike and convex. One can illustrate the same method on other classes.

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