Inequalities Involving the Derivative of Rational Functions With Prescribed Poles
This paper gives an upper bound of a modulus of the derivative of rational functions. rz=z−z0shz/wz∈Rm,n, where rz has exactly n poles a1,a2,⋯,an and all the zeros of rz lie in Dk∪Dk+,k≥1 except the zeros of order s at z0,z0<k. Moreover, we give an upper bound of a modulus of the derivative of ra...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2024-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/5189314 |
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| Summary: | This paper gives an upper bound of a modulus of the derivative of rational functions. rz=z−z0shz/wz∈Rm,n, where rz has exactly n poles a1,a2,⋯,an and all the zeros of rz lie in Dk∪Dk+,k≥1 except the zeros of order s at z0,z0<k. Moreover, we give an upper bound of a modulus of the derivative of rational functions. rz=z−zvsvz−zv−1sv−1⋯z−z0s0hz/wz, where rz has the zeros z0,z1,⋯,zv with zi<k for 0≤i≤v and the remaining n−s0+s1+⋯+sv zeros lie in Dk∪Dk+. 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. |
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| ISSN: | 1687-0042 |