فهرست نشریات علمی دسترسی آزاد ایران

In this paper, we investigate a generalized class of complex polynomials of the form G(z) = a_n z^n +\sum_{v=t}^{n} a_{n-v}z^{n-v}, 1\leq t \leq n, whose zeros are constrained to lie within or on the boundary of the disk  |z|\leq k, k\leq 1.  We establish new  Bernstein-type inequalities for such polynomials, extending and improving earlier results due to Jain [6], Aziz and Rather [4]. Several known inequalities follow as special cases, and the results have implications for the growth estimates and derivative bounds of analytic functions within specified domains.