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Gauss Lucas theorem and Bernstein-type inequalities for polynomials


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According to Gauss-Lucas theorem, every convex set containing all the zeros of a polynomial also contains all its critical points. This result is of central importance in the geometry of critical points in the analytic theory of polynomials. In this paper, an extension of Gauss-Lucas theorem is obtained and as an application some generalizations of Bernstein-type polynomial inequalities are also established.

eISSN:
2066-7752
Language:
English
Publication timeframe:
2 times per year
Journal Subjects:
Mathematics, General Mathematics