This paper gives an upper bound of a modulus of the derivative of rational functions. where r ( z ) has exactly n poles a 1 , a 2 , ⋯, a n and all the zeros of r ( z ) lie in k ≥ 1 except the zeros of order s at z 0 , | z 0 | &lt; k . Moreover, we give an upper bound of a modulus of the derivative of rational functions. , where r ( z ) has the zeros z 0 , z 1 , ⋯, z v with | z i | &lt; k for 0 ≤ i ≤ v and the remaining n − ( s 0 + s 1 +⋯+ s v ) zeros lie in Additionally, we provide proofs for several results that not only generalize certain inequalities for rational functions with restricted zeros but also offer refinements of certain polynomial inequalities as special cases.

Preeti Gupta

Journal of Applied Mathematics

JOURNAL OF APPLIED MATHEMATICS 是一本专业期刊，致力于在应用、计算和工业数学的所有领域发表原创研究论文和评论文章。

The Journal of Applied Mathematics is a professional journal dedicated to publishing original research papers and review articles in all areas of applied, computational, and industrial mathematics.

《Journal of Applied Mathematics》是一本专业期刊，专注于应用、计算和工业数学领域，发表原创研究论文和评论文章。

Inequalities Involving the Derivative of Rational Functions With Prescribed Poles

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Journal Info

Category	Quartile
MATHEMATICS, INTERDISCIPLINARY APPLICATIONS	3