Partial Sums of Generalized Class of Analytic Functions Involving Hurwitz-Lerch Zeta Function
Let fn(z)=z+∑k=2nakzk be the sequence of partial sums of the analytic function f(z)=z+∑k=2∞akzk. In this paper, we determine sharp lower bounds for ℜ{f(z)/fn(z)}, ℜ{fn(z)/f(z)}, ℜ{f′(z)/fn′(z)}, and ℜ{fn′(z)/f′(z)}. The usefulness of the main result not only provides the unification of the results...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/849250 |
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| author | G. Murugusundaramoorthy K. Uma M. Darus |
| author_facet | G. Murugusundaramoorthy K. Uma M. Darus |
| author_sort | G. Murugusundaramoorthy |
| collection | DOAJ |
| description | Let fn(z)=z+∑k=2nakzk be the sequence of partial sums of the analytic function f(z)=z+∑k=2∞akzk. In this paper, we determine sharp lower bounds for ℜ{f(z)/fn(z)}, ℜ{fn(z)/f(z)}, ℜ{f′(z)/fn′(z)}, and ℜ{fn′(z)/f′(z)}. The usefulness of the main result not
only provides the unification of the results discussed in the literature but also generates certain
new results. |
| format | Article |
| id | doaj-art-7abc31dee4084db993bb6fae62204c41 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-7abc31dee4084db993bb6fae62204c412025-02-03T01:10:21ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/849250849250Partial Sums of Generalized Class of Analytic Functions Involving Hurwitz-Lerch Zeta FunctionG. Murugusundaramoorthy0K. Uma1M. Darus2School of Advanced Sciences, VIT University, Vellore 632014, IndiaSchool of Advanced Sciences, VIT University, Vellore 632014, IndiaSchool of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, MalaysiaLet fn(z)=z+∑k=2nakzk be the sequence of partial sums of the analytic function f(z)=z+∑k=2∞akzk. In this paper, we determine sharp lower bounds for ℜ{f(z)/fn(z)}, ℜ{fn(z)/f(z)}, ℜ{f′(z)/fn′(z)}, and ℜ{fn′(z)/f′(z)}. The usefulness of the main result not only provides the unification of the results discussed in the literature but also generates certain new results.http://dx.doi.org/10.1155/2011/849250 |
| spellingShingle | G. Murugusundaramoorthy K. Uma M. Darus Partial Sums of Generalized Class of Analytic Functions Involving Hurwitz-Lerch Zeta Function Abstract and Applied Analysis |
| title | Partial Sums of Generalized Class of Analytic Functions Involving Hurwitz-Lerch Zeta Function |
| title_full | Partial Sums of Generalized Class of Analytic Functions Involving Hurwitz-Lerch Zeta Function |
| title_fullStr | Partial Sums of Generalized Class of Analytic Functions Involving Hurwitz-Lerch Zeta Function |
| title_full_unstemmed | Partial Sums of Generalized Class of Analytic Functions Involving Hurwitz-Lerch Zeta Function |
| title_short | Partial Sums of Generalized Class of Analytic Functions Involving Hurwitz-Lerch Zeta Function |
| title_sort | partial sums of generalized class of analytic functions involving hurwitz lerch zeta function |
| url | http://dx.doi.org/10.1155/2011/849250 |
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