Acknowledgement
We are thankful to NIT, Manipur for providing us financial support. We are also grateful to the referee for his/her useful suggestions.
References
- A. Aziz and N.A. Rather, Some Zygmund type Lq inequalities for polynomials, J. Math. Anal. Appl., 289 (2004), 14-29. https://doi.org/10.1016/S0022-247X(03)00530-4
- K.K. Dewan and A. Mir, Note on a theorem of S. Bernstein, Southeast Asian Bull. Math., 31 (2007), 691-695.
- N.K. Govil, On a theorem of S. Bernstein, J. Math. Phy. Sci., 14(2) (1980), 183-187.
- N.K. Govil and Q.I. Rahman, Functions of exponential type not vanishing in a half-plane and related polynomials, Trans. Amer. Math. Soc., 137 (1969), 501-517. https://doi.org/10.2307/1994818
- P.D. Lax, Proof of a conjecture of P. Erdos on the derivative of a polynomial, Bull. Amer. Math. Soc., 50 (1969), 509-513. https://doi.org/10.1090/S0002-9904-1944-08177-9
- M.A. Malik, On the derivative of a polynomial, J. London Math. Soc., 1 (1969), 57-60. https://doi.org/10.1112/jlms/s2-1.1.57
- G. Polya and G. Szego, Aufgaben and Lehrsatze aus der analysis, Springer, Berlin, 1925.
- M. Riesz, Uber einen Satz des Herrn Serge Bernstein, Acta Math., 40 (1916), 337-347. https://doi.org/10.1007/BF02418550
- A.C. Schaeffer, Inequalities of A. Markoff and S. Bernstein for polynomials and related functions, Bull. Amer. Math. Soc., 47 (1941), 565-579. https://doi.org/10.1090/S0002-9904-1941-07510-5