Abstract
In this paper, we obtain some results concerning the zeros of a class of generalized derivatives which are analogous to those for the ordinary derivative and the polar derivatives of polynomials.
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Notes
Can be easily verified by taking \(f(z)=z^2+4\), \(\psi (w)=\frac{w}{w+1}\) and \(g(w)=5w^2+8w+4\).
This is precisely the reason that the conclusion of Theorem B failed to hold for \(f(z)=z^3-8\) and \(C=\{z\in \hat{\mathbb {C}}:|z|\ge 1\}\).
References
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Marden, M.: Geometry of Polynomials. American Mathematical Society, Providence (1996)
Rahman, Q.I., Schmeisser, G.: Analytic Theory of Polynomials. Oxford University Press, New York (2002)
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The authors are extremely grateful to the anonymous referee(s) for valuable suggestions regarding the paper.
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Rather, N.A., Iqbal, A. & Dar, I. On the zeros of a class of generalized derivatives. Rend. Circ. Mat. Palermo, II. Ser 70, 1201–1211 (2021). https://doi.org/10.1007/s12215-020-00552-z
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DOI: https://doi.org/10.1007/s12215-020-00552-z