A note on neighborhoods of analytic functions having positive real part
Let P denote the set of all functions analytic in the unit disk D={z||z|<1} having the form p(z)=1+∑k=1∞pkzk with Re{p(z)}>0. For δ≥0, let Nδ(p) be those functions q(z)=1+∑k=1∞qkzk analytic in D with ∑k=1∞|pk−qk|≤δ. We denote by P′ the class of functions analytic in D having the form p(z)=1+∑k...
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| Format: | Article |
| Language: | English |
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Wiley
1990-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171290000643 |
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| _version_ | 1850161144425086976 |
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| author | Janice B. Walker |
| author_facet | Janice B. Walker |
| author_sort | Janice B. Walker |
| collection | DOAJ |
| description | Let P denote the set of all functions analytic in the unit disk D={z||z|<1} having the form p(z)=1+∑k=1∞pkzk with Re{p(z)}>0. For δ≥0, let Nδ(p) be those functions q(z)=1+∑k=1∞qkzk analytic in D with ∑k=1∞|pk−qk|≤δ. We denote by P′ the class of functions analytic in D having the form p(z)=1+∑k=1∞pkzk with Re{[zp(z)]′}>0. We show that P′ is a subclass of P and detemine δ so that Nδ(p)⊂P for p∈P′. |
| format | Article |
| id | doaj-art-fbecc05379ca4568b57a406f52155d4e |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1990-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-fbecc05379ca4568b57a406f52155d4e2025-08-20T02:22:56ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251990-01-0113342542910.1155/S0161171290000643A note on neighborhoods of analytic functions having positive real partJanice B. Walker0Department of Mathematics, Xavier University, Cincinnati 45207, Ohio, USALet P denote the set of all functions analytic in the unit disk D={z||z|<1} having the form p(z)=1+∑k=1∞pkzk with Re{p(z)}>0. For δ≥0, let Nδ(p) be those functions q(z)=1+∑k=1∞qkzk analytic in D with ∑k=1∞|pk−qk|≤δ. We denote by P′ the class of functions analytic in D having the form p(z)=1+∑k=1∞pkzk with Re{[zp(z)]′}>0. We show that P′ is a subclass of P and detemine δ so that Nδ(p)⊂P for p∈P′.http://dx.doi.org/10.1155/S0161171290000643functions having positive real part (Carathéodory class)subordinate functionδ-neighborhoodand convolution (Hadamard product). |
| spellingShingle | Janice B. Walker A note on neighborhoods of analytic functions having positive real part International Journal of Mathematics and Mathematical Sciences functions having positive real part (Carathéodory class) subordinate function δ-neighborhood and convolution (Hadamard product). |
| title | A note on neighborhoods of analytic functions having positive real part |
| title_full | A note on neighborhoods of analytic functions having positive real part |
| title_fullStr | A note on neighborhoods of analytic functions having positive real part |
| title_full_unstemmed | A note on neighborhoods of analytic functions having positive real part |
| title_short | A note on neighborhoods of analytic functions having positive real part |
| title_sort | note on neighborhoods of analytic functions having positive real part |
| topic | functions having positive real part (Carathéodory class) subordinate function δ-neighborhood and convolution (Hadamard product). |
| url | http://dx.doi.org/10.1155/S0161171290000643 |
| work_keys_str_mv | AT janicebwalker anoteonneighborhoodsofanalyticfunctionshavingpositiverealpart AT janicebwalker noteonneighborhoodsofanalyticfunctionshavingpositiverealpart |