On the Inequality Theorem for a Wider Class of Analytic Functions with Hadamard Product
In this paper, we discuss a well known class studied by Ramesha in 1995 and later by Janteng in 2006, and we then extend the class to a wider class of functions f denoted by nαβ,γ which are normalized and univalent, in the unit disk D=z∈ℂ:z<1 satisfying the condition Reαz2f′′z/gz+zf′z/gz>β, 0≤...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2022/8381624 |
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| Summary: | In this paper, we discuss a well known class studied by Ramesha in 1995 and later by Janteng in 2006, and we then extend the class to a wider class of functions f denoted by nαβ,γ which are normalized and univalent, in the unit disk D=z∈ℂ:z<1 satisfying the condition Reαz2f′′z/gz+zf′z/gz>β, 0≤α<1,0≤β<1, where g is analytic function in D, such that gz≠0, with a new condition that is introduced. The main purpose of this paper is to give an estimate for the same a3−μa22 when f belongs to the class nαβ,γ. |
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| ISSN: | 1687-0425 |