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Applications of Fractional q‐Calculus to Certain Subclass of Analytic p‐Valent Functions with Negative Coefficients

Author

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  • Ben Wongsaijai
  • Nattakorn Sukantamala

Abstract

By making use of the concept of fractional q‐calculus, we firstly define q‐extension of the generalization of the generalized Al‐Oboudi differential operator. Then, we introduce new class of q‐analogue of p‐valently closed‐to‐convex function, and, consequently, new class by means of this new general differential operator. Our main purpose is to determine the general properties on such class and geometric properties for functions belonging to this class with negative coefficient. Further, the q‐extension of interesting properties, such as distortion inequalities, inclusion relations, extreme points, radii of generalized starlikeness, convexity and close‐to‐convexity, quasi‐Hadamard properties, and invariant properties, is obtained. Finally, we briefly indicate the relevant connections of our presented results to the former results.

Suggested Citation

  • Ben Wongsaijai & Nattakorn Sukantamala, 2015. "Applications of Fractional q‐Calculus to Certain Subclass of Analytic p‐Valent Functions with Negative Coefficients," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnlaaa:v:2015:y:2015:i:1:n:273236
    DOI: 10.1155/2015/273236
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    References listed on IDEAS

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    1. R. M. El-Ashwah & M. K. Aouf & A. A. M. Hassan & A. H. Hassan, 2013. "A New Class of Analytic Functions Defined by Using Salagean Operator," International Journal of Analysis, Hindawi, vol. 2013, pages 1-10, February.
    2. Khalifa Al-Shaqsi & Maslina Darus & Olubunmi Abidemi Fadipe-Joseph, 2010. "A New Subclass of Salagean-Type Harmonic Univalent Functions," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-12, February.
    3. 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.
    4. G. Murugusundaramoorthy & C. Selvaraj & O. S. Babu, 2013. "Subclasses of Starlike Functions Associated with Fractional -Calculus Operators," Journal of Complex Analysis, Hindawi, vol. 2013, pages 1-8, April.
    5. Khalifa Al-Shaqsi & Maslina Darus & Olubunmi Abidemi Fadipe-Joseph, 2010. "A New Subclass of Salagean‐Type Harmonic Univalent Functions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
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    Cited by:

    1. Ben Wongsaijai & Nattakorn Sukantamala, 2016. "Certain Properties of Some Families of Generalized Starlike Functions with respect to q‐Calculus," Abstract and Applied Analysis, John Wiley & Sons, vol. 2016(1).

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