Inequalities for the generalized polar derivative of a polynomial
نویسندگان
1 Department of Mathematics, University of Kashmir, Srinagar-190006, India
2 Department of Mathematics, University of Kashmir, Srinagar-190006, India
3 Department of Applied Sciences, Institute of Technology, University of Kashmir, Srinagar-190006, India
4 Department of Mathematics, University of Kashmir, Srinagar-190006, India
doi
10.22075/ijnaa.2024.24504.2759چکیده
Recently Rather et al. [18] considered the generalized polar derivative and studied the relative position of zeros of the generalized polar derivative with respect to the zeros of the polynomial. In this paper, by taking into account the size of the constant term and the leading coefficient of the polynomial $P(z)$, we obtain some lower bound estimates for the generalized polar derivative of certain polynomials, which refine and generalize various results due to Aziz and Rather, Malik, Tur\'{a}n, Dubinin, Govil and others.
