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Let $${\mathcal{U}}$$ denote the set of all normalized analytic functions f in the unit disk $${|z| < 1}$$ satisfying the condition $$\left| \left(\frac{z}{f(z)}\right)^{2} f'(z) - 1 \right| < 1 {\rm for} |z| < 1.$$ It is well-known that $${\mathcal{U}}$$ is contained in the class $${\mathcal{S}}$$ of univalent analytic functions in $${\mathbb{D}}$$ . In this paper...
. Based on the Borel transformation and the Hadamard multiplication theorem on singularities on the convolution of holomorphic functions, results on the growth of entire functions defined by convolution of an entire function of exponential type with a function holomorphic at the origin are obtained.
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