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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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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| author | Preeti Gupta |
| author_facet | Preeti Gupta |
| author_sort | Preeti Gupta |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0ee6f37c43b94795abbbc6f0d3d0cad9 |
| institution | Kabale University |
| issn | 1687-0042 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-0ee6f37c43b94795abbbc6f0d3d0cad92024-12-11T00:00:01ZengWileyJournal of Applied Mathematics1687-00422024-01-01202410.1155/2024/5189314Inequalities Involving the Derivative of Rational Functions With Prescribed PolesPreeti Gupta0Department of Applied MathematicsThis 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.http://dx.doi.org/10.1155/2024/5189314 |
| spellingShingle | Preeti Gupta Inequalities Involving the Derivative of Rational Functions With Prescribed Poles Journal of Applied Mathematics |
| title | Inequalities Involving the Derivative of Rational Functions With Prescribed Poles |
| title_full | Inequalities Involving the Derivative of Rational Functions With Prescribed Poles |
| title_fullStr | Inequalities Involving the Derivative of Rational Functions With Prescribed Poles |
| title_full_unstemmed | Inequalities Involving the Derivative of Rational Functions With Prescribed Poles |
| title_short | Inequalities Involving the Derivative of Rational Functions With Prescribed Poles |
| title_sort | inequalities involving the derivative of rational functions with prescribed poles |
| url | http://dx.doi.org/10.1155/2024/5189314 |
| work_keys_str_mv | AT preetigupta inequalitiesinvolvingthederivativeofrationalfunctionswithprescribedpoles |