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On univalent functions defined by a generalized Sălăgean operator

Author

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  • F. M. Al-Oboudi

Abstract

We introduce a class of univalent functions R n ( λ , α ) defined by a new differential operator D n f ( z ) , n ∈ ℕ 0 = { 0 , 1 , 2 , … } , where D 0 f ( z ) = f ( z ) , D 1 f ( z ) = ( 1 − λ ) f ( z ) + λ z f ′ ( z ) = D λ f ( z ) , λ ≥ 0 , and D n f ( z ) = D λ ( D n − 1 f ( z ) ) . Inclusion relations, extreme points of R n ( λ , α ) , some convolution properties of functions belonging to R n ( λ , α ) , and other results are given.

Suggested Citation

  • F. M. Al-Oboudi, 2004. "On univalent functions defined by a generalized Sălăgean operator," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-8, January.
    • Handle: RePEc:hin:jijmms:172525
    DOI: 10.1155/S0161171204108090
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    Cited by:

    1. Matthew Olanrewaju Oluwayemi & Kaliappan Vijaya & Adriana Cătaş, 2022. "Certain Properties of a Class of Functions Defined by Means of a Generalized Differential Operator," Mathematics, MDPI, vol. 10(2), pages 1-10, January.
    2. Malathi, V. & Vijaya, K., 2022. "Subclass of analytic functions involving Erdély–Kober type integral operator in conic regions and applications to neutrosophic Poisson distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    3. Rabha W. Ibrahim & Rafida M. Elobaid & Suzan J. Obaiys, 2020. "Symmetric Conformable Fractional Derivative of Complex Variables," Mathematics, MDPI, vol. 8(3), pages 1-13, March.
    4. T. M. Seoudy, 2013. "On Certain Classes of Harmonic -Valent Functions Defined by an Integral Operator," International Journal of Analysis, Hindawi, vol. 2013, pages 1-7, February.
    5. Sondekola Rudra Swamy & Alina Alb Lupaş & Nanjundan Magesh & Yerragunta Sailaja, 2023. "Properties of a Special Holomorphic Function Linked with a Generalized Multiplier Transformation," Mathematics, MDPI, vol. 11(19), pages 1-10, September.
    6. Ayotunde Olajide Lasode & Timothy Oloyede Opoola & Isra Al-Shbeil & Timilehin Gideon Shaba & Huda Alsaud, 2023. "Concerning a Novel Integral Operator and a Specific Category of Starlike Functions," Mathematics, MDPI, vol. 11(21), pages 1-17, November.
    7. Sarfraz Nawaz Malik & Nazar Khan & Ferdous M. O. Tawfiq & Mohammad Faisal Khan & Qazi Zahoor Ahmad & Qin Xin, 2023. "Fuzzy Differential Subordination Associated with a General Linear Transformation," Mathematics, MDPI, vol. 11(22), pages 1-17, November.
    8. R. M. El-Ashwah & M. K. Aouf & S. M. El-Deeb, 2013. "Differential Subordination for Certian Subclasses of -Valent Functions Assoicated with Generalized Linear Operator," Journal of Mathematics, Hindawi, vol. 2013, pages 1-8, March.
    9. Ekram E. Ali & Hari M. Srivastava & Abeer M. Albalahi, 2023. "Subclasses of p -Valent κ -Uniformly Convex and Starlike Functions Defined by the q -Derivative Operator," Mathematics, MDPI, vol. 11(11), pages 1-19, June.
    10. Ekram E. Ali & Georgia Irina Oros & Shujaat Ali Shah & Abeer M. Albalahi, 2023. "Applications of q -Calculus Multiplier Operators and Subordination for the Study of Particular Analytic Function Subclasses," Mathematics, MDPI, vol. 11(12), pages 1-15, June.
    11. Abdel Moneim Y. Lashin & Mohamed K. Aouf, 2022. "Hadamard Product of Certain Multivalent Analytic Functions with Positive Real Parts," Mathematics, MDPI, vol. 10(9), pages 1-9, May.
    12. Daniel Breaz & Shahid Khan & Ferdous M. O. Tawfiq & Fairouz Tchier, 2023. "Applications of Fuzzy Differential Subordination to the Subclass of Analytic Functions Involving Riemann–Liouville Fractional Integral Operator," Mathematics, MDPI, vol. 11(24), pages 1-22, December.
    13. Abbas Kareem Wanas & Luminiţa-Ioana Cotîrlă, 2022. "Applications of ( M , N )-Lucas Polynomials on a Certain Family of Bi-Univalent Functions," Mathematics, MDPI, vol. 10(4), pages 1-11, February.
    14. Ekram Elsayed Ali & Teodor Bulboacă, 2020. "Subclasses of Multivalent Analytic Functions Associated with a q -Difference Operator," Mathematics, MDPI, vol. 8(12), pages 1-8, December.
    15. Daniel Breaz & Kadhavoor R. Karthikeyan & Elangho Umadevi, 2022. "Subclasses of Multivalent Meromorphic Functions with a Pole of Order p at the Origin," Mathematics, MDPI, vol. 10(4), pages 1-15, February.
    16. Ibtisam Aldawish & Tariq Al-Hawary & B. A. Frasin, 2020. "Subclasses of Bi-Univalent Functions Defined by Frasin Differential Operator," Mathematics, MDPI, vol. 8(5), pages 1-11, May.
    17. Serap Bulut, 2013. "Mapping Properties of Some Classes of Analytic Functions under Certain Integral Operators," Journal of Mathematics, Hindawi, vol. 2013, pages 1-7, January.
    18. Wafaa Y. Kota & Rabha M. El-Ashwah & Nicoleta Breaz, 2023. "Application of the Quasi-Hadamard Product to Subclasses of Analytic Functions Involving the q -Difference Operator," Mathematics, MDPI, vol. 11(10), pages 1-9, May.
    19. Loriana Andrei & Vasile-Aurel Caus, 2024. "Subordinations Results on a q -Derivative Differential Operator," Mathematics, MDPI, vol. 12(2), pages 1-20, January.
    20. Nazar Khan & Shahid Khan & Qin Xin & Fairouz Tchier & Sarfraz Nawaz Malik & Umer Javed, 2023. "Some Applications of Analytic Functions Associated with q -Fractional Operator," Mathematics, MDPI, vol. 11(4), pages 1-17, February.

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