Research article

Classes of analytic functions involving the q-Ruschweyh operator and q-Bernardi operator

  • Received: 22 September 2024 Revised: 10 November 2024 Accepted: 13 November 2024 Published: 22 November 2024
  • MSC : 30C45

  • In this paper, we introduced and studied two new classes of analytic functions using the concepts of subordination and q-calculus. We established inclusion relations for these q-classes and integral-preserving properties associated with the q-integral operator. We also determined certain convolution properties.

    Citation: Khadeejah Rasheed Alhindi, Khalid M. K. Alshammari, Huda Ali Aldweby. Classes of analytic functions involving the q-Ruschweyh operator and q-Bernardi operator[J]. AIMS Mathematics, 2024, 9(11): 33301-33313. doi: 10.3934/math.20241589

    Related Papers:

  • In this paper, we introduced and studied two new classes of analytic functions using the concepts of subordination and q-calculus. We established inclusion relations for these q-classes and integral-preserving properties associated with the q-integral operator. We also determined certain convolution properties.



    加载中


    [1] M. E. H. Ismail, E. Merkes, D. A. Styer, A generalization of starlike functions, Complex Variab. Theory Appl., 14. (1990), 77–84. https://doi.org/10.1080/17476939008814407 doi: 10.1080/17476939008814407
    [2] S. Ruscheweyh, Extension of Szegö's theorem on the sections of univalent functions, SIAM J. Math. Anal., 19. (1988), 1442–1449. https://doi.org/10.1137/0519107 doi: 10.1137/0519107
    [3] E. Bernardi, A. Bove, Geometric results for a class of hyperbolic operators with double characteristics, Commun. Partial Differ. Equations, 13. (1988), 61–86. https://doi.org/10.1080/03605308808820538 doi: 10.1080/03605308808820538
    [4] A. Mohammed, M. Darus, A generalized operator involving the $q$-hypergeometric function, Mat. Vesnik, 65. (2013), 454–465.
    [5] H. Aldweby, M. Darus, Some subordination results on $q$-analogue of the Ruscheweyh differential operator, Abstr. Appl. Anal., 2014. (2014), 958563. https://doi.org/10.1155/2014/958563 doi: 10.1155/2014/958563
    [6] M. Govindaraj, S. Sivasubramanian, On a class of analytic functions related to conic domains involving $q$-calculus, Anal. Math., 43. (2017), 475–487. https://doi.org/10.1007/s10476-017-0206-5 doi: 10.1007/s10476-017-0206-5
    [7] B. Khan, H. M. Srivastava, S. Arjika, S. Khan, N. Khan, Q. Z. Ahmad, A certain $q$-Ruscheweyh type derivative operator and its applications involving multivalent functions, Adv. Differ. Equations, 2021. (2021), 279. https://doi.org/10.1186/s13662-021-03441-6 doi: 10.1186/s13662-021-03441-6
    [8] K. Alshammari, M. Darus, Applications of the $q$-Ruscheweyh symmetric differential operator in a class of starlike functions, Comput. Sci., 18. (2023), 707–718.
    [9] K. A. Selvakumaran, S. D. Purohit, A. Secer, M. Bayram, Convexity of certain $q$-integral operators of $p$-valent functions, Abstr. Appl. Anal., 2014. (2014), 925902. https://doi.org/10.1155/2014/925902 doi: 10.1155/2014/925902
    [10] K. I. Noor, S. Riaz, M. A. Noor, On $q$-Bernardi integral operator, TWMS J. Pure Appl. Math., 8. (2017), 3–11.
    [11] M. Arif, M. U. Haq, J. L. Liu, A subfamily of univalent functions associated with $q$-analogue of Noor integral operator, J. Funct. Spaces, 2018. (2018), 3818915. https://doi.org/10.1155/2018/3818915 doi: 10.1155/2018/3818915
    [12] S. A. Shah, K. I. Noor, Study on the $q$-analogue of a certain family of linear operators, Turk. J. Math., 43. (2019), 2707–2714. https://doi.org/10.3906/mat-1907-41 doi: 10.3906/mat-1907-41
    [13] K. R. Alhindi, Convex families of $q$-derivative meromorphic functions involving the polylogarithm function, Symmetry, 15. (2023), 1388. https://doi.org/10.3390/sym15071388 doi: 10.3390/sym15071388
    [14] S. S. Miller, P. T. Mocanu, Differential subordinations theory and applications, CRC Press, 2000. https://doi.org/10.1201/9781482289817
    [15] A. Aral, V. Gupta, R. P. Agarwal, Applications of $q$-calculus in operator theory, Springer, 2013. https://doi.org/10.1007/978-1-4614-6946-9
    [16] F. H. Jackson, On $q$-difference integrals, Q. J. Pure Appl. Math., 41. (1910), 193–203.
    [17] H. Exton, $q$-hypergeometric functions and applications, Ellis Horwood Limited, 1983. https://doi.org/10.1016/0378-4754(84)90050-8
    [18] D. Breaz, A. A. Alahmari, L. I. Cotîrlă, S. A. Shah, On generalizations of the close-to-convex functions associated with $q$-Srivastava-Attiya operator, Mathematics, 11. (2023), 2022. https://doi.org/10.3390/math11092022 doi: 10.3390/math11092022
  • Reader Comments
  • © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(95) PDF downloads(25) Cited by(0)

Article outline

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog