On coefficient bounds of a certain class of p-valent λ-spiral functions of order α
Let Sλ(A,B,p,α)(|λ|<π2, −1≦A<B≦1 and 0≦α<p), denote the class of functions f(z)=zp+∑n=p+1∞anzn analytic in U={z:|z|<1}, which satisfy for z=reiθ∈Ueiλsecλzf′(z)f(z)−ip tanλ=p+[pB+(A−B)(p−α)]w(z)1+Bw(z), w(z) is analytic in U with w(0)=0 and |w(z)|≦|z| for z∈U. In this paper we obtain the...
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| Language: | English |
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Wiley
1987-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171287000322 |
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| author | M. K. Aouf |
| author_facet | M. K. Aouf |
| author_sort | M. K. Aouf |
| collection | DOAJ |
| description | Let Sλ(A,B,p,α)(|λ|<π2, −1≦A<B≦1 and 0≦α<p), denote the class of functions f(z)=zp+∑n=p+1∞anzn analytic in U={z:|z|<1}, which satisfy for z=reiθ∈Ueiλsecλzf′(z)f(z)−ip tanλ=p+[pB+(A−B)(p−α)]w(z)1+Bw(z),
w(z) is analytic in U with w(0)=0 and |w(z)|≦|z| for z∈U. In this paper we obtain the bounds of an and we maximize |ap+2−μap+12| over the class Sλ(A,B,p,α) for complex values of μ. |
| format | Article |
| id | doaj-art-21198ee3bf134ba08f25bb979d370670 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1987-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-21198ee3bf134ba08f25bb979d3706702025-02-03T05:59:09ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251987-01-0110225926610.1155/S0161171287000322On coefficient bounds of a certain class of p-valent λ-spiral functions of order αM. K. Aouf0Department of Mathematics, Faculty of Science, University of Mansoura, Mansoura, EgyptLet Sλ(A,B,p,α)(|λ|<π2, −1≦A<B≦1 and 0≦α<p), denote the class of functions f(z)=zp+∑n=p+1∞anzn analytic in U={z:|z|<1}, which satisfy for z=reiθ∈Ueiλsecλzf′(z)f(z)−ip tanλ=p+[pB+(A−B)(p−α)]w(z)1+Bw(z), w(z) is analytic in U with w(0)=0 and |w(z)|≦|z| for z∈U. In this paper we obtain the bounds of an and we maximize |ap+2−μap+12| over the class Sλ(A,B,p,α) for complex values of μ.http://dx.doi.org/10.1155/S0161171287000322p-valentanalyticboundsλ-spirallike functions of orderα. |
| spellingShingle | M. K. Aouf On coefficient bounds of a certain class of p-valent λ-spiral functions of order α International Journal of Mathematics and Mathematical Sciences p-valent analytic bounds λ-spirallike functions of orderα. |
| title | On coefficient bounds of a certain class of p-valent λ-spiral functions of order α |
| title_full | On coefficient bounds of a certain class of p-valent λ-spiral functions of order α |
| title_fullStr | On coefficient bounds of a certain class of p-valent λ-spiral functions of order α |
| title_full_unstemmed | On coefficient bounds of a certain class of p-valent λ-spiral functions of order α |
| title_short | On coefficient bounds of a certain class of p-valent λ-spiral functions of order α |
| title_sort | on coefficient bounds of a certain class of p valent λ spiral functions of order α |
| topic | p-valent analytic bounds λ-spirallike functions of orderα. |
| url | http://dx.doi.org/10.1155/S0161171287000322 |
| work_keys_str_mv | AT mkaouf oncoefficientboundsofacertainclassofpvalentlspiralfunctionsofordera |