A Refinement of Schwarz's Lemma and its Applications

By using the value of the second derivative of the function at 0, along with the values of the function and its rst derivative at 0, we have obtained a re nement of well known Schwarz's lemma and have used this re nement to obtain re nements, of Aziz and Rather's inequalities [2004] for a polynomial of degree n having no zeros in |z| < k, (k >= 1).

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