References
- V.V. Arestov, On integral inequalities for trigonometric polynomials and their derivative, IZV. Akad. Nauk. SSSR. Ser. Math., 45(2) (1981), 3-22.
- A. Aziz, Inequalities for the polar derivative of a polynomial, J. Approx. Theory, 55(2) (1988), 183-193. https://doi.org/10.1016/0021-9045(88)90085-8
- 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
- S. Bernstein, "Lecons Sur Les Proprietes extremales et la meilleure approximation desfunctions analytiques d'une fonctions reele," Gauthier-Villars (Paris, 1926).
- B. Chanam, Lr inequalities for polynomials, Southeast Asian Bulletin of Mathematics, 42 (2018), 825-832.
- B. Chanam, K.B. Devi and K. Krishnadas, Some inequalities concerning polar derivative of a polynomial, Int. J. Pure and Appl. Math. Sci., 14(1) (2021), 9-19.
- I. Das, R. Soraisam, M.S. Singh, N.K. Singha and B. Chanam, Inequalities for complex polynomial with restricted zeros, Nonlinear Funct. Anal. Appl., 28(4) (2023), 943-956.
- 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.
- K.K. Dewan, A. Bhat and M.S. Pukhta, Inequalities concerning the Lr norm of a polynomial, J. Math. Anal. Appl., 224 (1998), 14-21. https://doi.org/10.1006/jmaa.1998.5980
- K.K. Dewan, N. Singh and A. Mir, Extensions of some polynomial inequalities to the polar derivative, J. Math. Anal. Appl., 352 (2009), 807-815. https://doi.org/10.1016/j.jmaa.2008.10.056
- N.K. Govil and P. Kumar, On Lp inequalities involving polar derivative of a polynomial, Acta Math. Hungar., 152 (2017), 130-139 . https://doi.org/10.1007/s10474-017-0693-7
- I. Hussain and A. Liman, Generalization of certain inequalities concerning the polar derivative of a polynomial, Kragujav. J. Math., 47(4) (2023), 613-625. https://doi.org/10.46793/KgJMat2304.613H
- 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. Lond. Math. Soc., 1(2) (1969), 57-60. https://doi.org/10.1112/jlms/s2-1.1.57
- M. Marden, Geometry of Polynomials, Math. Surveys, Amer. Math. Soc., Providence, 3 1966.
- G.V. Milovanovic, A. Mir and A. Malik, Estimates for the polar derivative of a constrained polynomial on a disk, CUBO, Math. J., 24(3) (2022), 541-554. https://doi.org/10.56754/0719-0646.2403.0541
- G.V. Milovanovic, D.S. Mitrinovic and T.M. Rassias, Topics in Polynomials: Extremal Problems, Ineq. Zeros, World Scientific., Singapore, 1994.
- A. Mir, Bernstein-type integral inequalities for a certain class of polynomials, Mediterr. J. Math., 16(143) (2020), 1-11. https://doi.org/10.1007/s00009-019-1428-5
- M.A. Qazi, On the maximum modulus of polynomials, Proc. Amer. Math. Soc., 115(2) (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 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.
- M.S. Singh, N. Reingachand, M.T. Devi and B. Chanam, Lγ Inequalities for the polar derivative of polynomials, Malaysian J. Math. Sci., 17(3) (2023), 333-347. https://doi.org/10.47836/mjms.17.3.06
- 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