On the derivative of a polynomial
DOI:
https://doi.org/10.5269/bspm.41683Resumen
In this paper, we establish some inequalities for the complex polynomial. Our results constitute generalizations and refinements of some well-known polynomial inequalities.
Referencias
1. Aziz, A., Ahmad, N., Inequalities for the derivative of a polynomial, Proc. Indian Acad. Sci. (Math. Sci.) 107, 189-196, (1997).
2. Bidkham, M., Dewan, K. K., Inequalities for a polynomial and its derivative, J. Math. Anal. Appl. 166, 319-324, (1992).
3. Bidkham, M., Soleiman Mezerji, H. A., Some inequalities for the polar derivative of polynomials in complex domain, Complex Anal. Oper. Theory. 7, 1257-1266, (2013).
4. Dewan, K. K., Bidkham, M., On the Enestrom-Kakeya theorem, J. Math. Anal. Appl. 180, 29-36, (1993).
5. Dewan, K. K., Hans, S., On Extremal Properties for the derivative of polynomials, J. Math. Balkanica. 23, 27-35, (2009).
6. Chan, T. N., Malik, M. A., On Erdos-Lax theorem, Proc. Indian. Acad. Sci. 92, 191-193, (1983).
7. Khojastehnezhad, E., Bidkham, M., Inequalities for the polar derivative of a polynomial with S-fold zeros at the origin, Bull. Iran. Math. Soc. 43, 2153-2167, (2017).
8. Lax, P. D., Proof a conjecture of P. Erdos on the derivative of a polynomial, Bull. Amer. Math Soc. 50, 509-513, (1944).
9. Govil, N. K., On a theorem of Bernstein, Proc. Natl. Acad. Sci. 50, 50-52, (1980).
10. Govil, N. K., On a theorem of Bernstein, J. Math. Phy. Sci. 14, 183-187, (1980).
11. Govil, N. K., Rahman, Q. I., Functions of exponential type not vanishing in a half plane and related polynomials, Trans. Amer. Math. Soc. 137, 501-517, (1969).
12. Malik, M. A., On the derivative of a polynomial. J . London. Math. Soc. 2, 57-60, (1969).
13. Rahman, Q. I., Schmeisser, G., Analytic Theory of Polynomials, Oxford University Press, New York (2002).
14. Zireh, A., Generalization of certain well-known inequalities for the derivative of polynomials, Anal. Math. 41, 117-132, (2015).
2. Bidkham, M., Dewan, K. K., Inequalities for a polynomial and its derivative, J. Math. Anal. Appl. 166, 319-324, (1992).
3. Bidkham, M., Soleiman Mezerji, H. A., Some inequalities for the polar derivative of polynomials in complex domain, Complex Anal. Oper. Theory. 7, 1257-1266, (2013).
4. Dewan, K. K., Bidkham, M., On the Enestrom-Kakeya theorem, J. Math. Anal. Appl. 180, 29-36, (1993).
5. Dewan, K. K., Hans, S., On Extremal Properties for the derivative of polynomials, J. Math. Balkanica. 23, 27-35, (2009).
6. Chan, T. N., Malik, M. A., On Erdos-Lax theorem, Proc. Indian. Acad. Sci. 92, 191-193, (1983).
7. Khojastehnezhad, E., Bidkham, M., Inequalities for the polar derivative of a polynomial with S-fold zeros at the origin, Bull. Iran. Math. Soc. 43, 2153-2167, (2017).
8. Lax, P. D., Proof a conjecture of P. Erdos on the derivative of a polynomial, Bull. Amer. Math Soc. 50, 509-513, (1944).
9. Govil, N. K., On a theorem of Bernstein, Proc. Natl. Acad. Sci. 50, 50-52, (1980).
10. Govil, N. K., On a theorem of Bernstein, J. Math. Phy. Sci. 14, 183-187, (1980).
11. Govil, N. K., Rahman, Q. I., Functions of exponential type not vanishing in a half plane and related polynomials, Trans. Amer. Math. Soc. 137, 501-517, (1969).
12. Malik, M. A., On the derivative of a polynomial. J . London. Math. Soc. 2, 57-60, (1969).
13. Rahman, Q. I., Schmeisser, G., Analytic Theory of Polynomials, Oxford University Press, New York (2002).
14. Zireh, A., Generalization of certain well-known inequalities for the derivative of polynomials, Anal. Math. 41, 117-132, (2015).
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2020-10-11
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