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Journals / European Journal of Pure and Applied Mathematics (elektronik) / 2011 / Cilt: 4 - Sayı: 1

On new subclasses of analytic functions involving generalized differential and integral operators

Maslina DARUS
Rabha W. IBRAHIM
Pages
59–66
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Characterization and other properties of these classes are studied. 2000 Mathematics Subject Classifications: 30C45

📌 3 Key Takeaways

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Objective & Hypothesis:We define a generalized differential and integral operators on the class $frak{A}$ of analytic functions $f(z) = z + sum^{infty}_{n=2}a_nz^n$ in the unit disk $U := {z ∈ Bbb{C}:|z| < 1} involving k−th Hadamard product (convolution) as follows $D^k_{alpha,lambda}f(z)=z+sumlimits_{n=2}^{infty} [(n-1)(lambda-alpha)+n]^k a_n z^n, hspace {3mm} (z in U)$.
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Key Findings & Data:These operators are generalized for some of well known operators for example Salagean operator.
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Conclusion & Impact:Characterization and other properties of these classes are studied. 2000 Mathematics Subject Classifications: 30C45
🔬Design:Research Article
📍Scope:2000 Verileri
⚙️Variables:Domain Parameters

Abstract

We define a generalized differential and integral operators on the class $frak{A}$ of analytic functions $f(z) = z + sum^{infty}_{n=2}a_nz^n$ in the unit disk $U := {z ∈ Bbb{C}:|z| < 1} involving k−th Hadamard product (convolution) as follows $D^k_{alpha,lambda}f(z)=z+sumlimits_{n=2}^{infty} [(n-1)(lambda-alpha)+n]^k a_n z^n, hspace {3mm} (z in U)$. These operators are generalized for some of well known operators for example Salagean operator. New classes containing these operators are investigated. Characterization and other properties of these classes are studied. 2000 Mathematics Subject Classifications: 30C45

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Cite This Article

DARUS, M., IBRAHIM, R. W. (2022). On new subclasses of analytic functions involving generalized differential and integral operators. European Journal of Pure and Applied Mathematics (elektronik), Cilt: 4 - Sayı: 1, 59–66. https://ajindex.com/articles/511320

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References (14)

  1. M.H. Al-Abbadi and M. Darus, Differential Subordination Defined by New Generalised Derivative Operator for Analytic Functions, International Journal of Mathematics and Mathematical Sciences, Article ID 369078, 15 pages. 2010
  2. S. Bulut, Some properties for an integral operator defined by AL-Oboudi differential operator, J. Ineq. Pure Appl. Math., Vol 9, Art. 115, pp5. 2008
  3. M.Darus and K.Al-Shaqsi, On Subordinations for certain analytic functions associated with generalized integral operator. Lobachevskii Journal of Mathematics, 29 (2), 90-97. 2008
  4. M. Darus, R. W. Ibrahim, Coefficient Inequalities for a New Class of Univalent Functions, Lobachevskii Journal of Mathematics, 29(4), 221-229. 2008
  5. R. W. Ibrahim, M. Darus, Subordination and superordination for univalent solutions for fractional differential equations, J. Math. Anal. Appl., 345, 871-879. 2008
  6. R. W. Ibrahim, M. Darus, On Subordination Theorems for New Classes of Normalize Analytic Functions, Applied Mathematical Sciences, 56(2), 2785 - 2794. 2008
  7. R. W. Ibrahim, M. Darus, Diferential subordination results for new classes of the family E(, ), J. Ineq. Pure and Appl. Math., Volume 9, Issue 4, Article draft, 9 pp. 2009
  8. R. W. Ibrahim and M. Darus, Subordination and superordination for analytic functions involving fractional integral operator, Complex Variables and Elliptic Equations, 53(11), 1021-1031. 2008
  9. S. Owa, H. M. Srivastava, Some generalized convolution properties associated with certain subclasses of analytic functions, J. Ineq. Pure Appl. Math., 3(3), Article 42. 2002
  10. S. Owa, J. Nishiwaki, Coefficent estimate for certain classes of analytic functions, J. Ineq. Pure Appl. Math., 3( 5), Article 72. 2002
  11. G. S. Salagean, Subclasses of univalent functions, Lecture Notes in Math., 1013, Springer-Verlag, Berlin, 362-372. 1983
  12. B. A. Uralegaddi, A. R. Desai, Convolutions of univalent functions with positive coefficients, Tamkang J. Math., 29, 279-285, 1998
  13. B. A. Uralegaddi, M. D. Ganigi and S. M. Sarangi, Univalent functions with positive coefficients, Tamkang J. Math., 25, 225-230. 1994
  14. Ri-G. Xiang, Z.-Gang Wang and M. Darus, A family of integral operators preserving subordination and superordination, Bull. Malays. Math. Sci., (2) 33(1), 121-131. 2010.