과제정보
The authors wish to thank the referees for their valuable comments.
참고문헌
- V.V. Arestov, On inequalities for trigonometric polynomials and their derivative, IZV. Akad. Nauk. SSSR. Ser. Math., 45 (1981), 3-22.
- A. Aziz and N.A. Rather, Some Zygmund type Lp inequalities for polynomials, J. Math. Anal. Appl., 289 (2004), 14-29. https://doi.org/10.1016/S0022-247X(03)00530-4
- A. Aziz and W.M. Shah, Inequalities for a polynomial and its derivative, Math. Ineq. Appl., 3 (2004), 379-391.
- A. Aziz and B.A. Zargar, Inequalities for a polynomial and its derivative, Math. Ineq. Appl., 4 (1998), 543-550.
- M. Bidkham and K.K. Dewan, Inequalities for polynomial and its derivative, J. Math. Anal. Appl., 166 (1992), 319-324. https://doi.org/10.1016/0022-247X(92)90298-R
- N.G. de-Bruijn, Inequalities concerning polynomials in the complex domain, Ned-erl. Akad. Wetench. Proc. Ser. A, 50 (1947), 1265-1272; Indag. Math 9(1947), 591-598.
- R.B. Gardner and N.K. Govil, An Lp inequality for a polynomial and its derivative, J. Math. Anal. Appl., 194 (1995), 720-726. https://doi.org/10.1006/jmaa.1995.1325
- R.B. Gardner and A. Weems, A Bernstein-type of Lp inequality for a certain class of polynomials, J. Math. Anal. Appl., 219 (1998), 472-478. https://doi.org/10.1006/jmaa.1997.5838
- 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/10.1090/S0002-9947-1969-0236385-6
- P.D. Lax, Proof of a conjecture of P.Erdos on the derivative of a polynomial, Bull. Amer. Math. Soc., 50 (1944), 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.V. Milovanovic, D.S. Mitrinovic and Th. Rassias, Topics in polynomials: External problems, Inequalities, Zeros, World Scientific, Singapore, 1994.
- M.S. Pukhta, Ph.D Thesis, Submitted to the Jamia Millia Islamia, New Delhi, 1995.
- M.A. QAZI, On the maximum modulus of polynomials, Proc. Amer. Math. Soc., 115 (1992), 337-343. https://doi.org/10.1090/S0002-9939-1992-1113648-1
- Q.I. Rahman and G. Schmeisser, Lp inequalities for polynomials, J. Approx. Theory, 53 (1988), 26-32. https://doi.org/10.1016/0021-9045(88)90073-1
- N.A. Rather, Extremal properties and location of the zeros of polynomials, Ph.D Thesis, University of Kashmir, 1998.
- W. Rudin, Real and Complex Analysis, Tata McGraw-Hill Publishing Company(reprinted in India), 1977.
- A.C. Schaeffer,Inequalities of A. Markoff and S. N. Bernstein for polynomials and related functions, Bull. Amer. Math. Soc., 47 (1941), 565-579. https://doi.org/10.1090/S0002-9904-1941-07510-5
- A. Zygmund, A remark on conjugate series, Proc. London Math. Soc., 34 (1932), 392-400. https://doi.org/10.1112/plms/s2-34.1.392