Research article

Geometric properties of $ q $-spiral-like with respect to $ (\ell, \jmath) $-symmetric points

  • Received: 13 September 2022 Revised: 13 November 2022 Accepted: 25 November 2022 Published: 02 December 2022
  • MSC : 30C45, 30C50

  • In this paper, the concepts of $ (\ell, \jmath) $-symmetrical functions and the concept of $ q $-calculus are combined to define a new subclasses defined in the open unit disk. In particular. We look into a convolution property, and we'll use the results to look into our task even more, we deduce the sufficient condition, coefficient estimates investigate related neighborhood results for the class $ \mathcal{S}^{\ell, \jmath}_q(\lambda) $ and some interesting convolution results are also pointed out.

    Citation: Samirah Alzahrani, Fuad Alsarari. Geometric properties of $ q $-spiral-like with respect to $ (\ell, \jmath) $-symmetric points[J]. AIMS Mathematics, 2023, 8(2): 4141-4152. doi: 10.3934/math.2023206

    Related Papers:

  • In this paper, the concepts of $ (\ell, \jmath) $-symmetrical functions and the concept of $ q $-calculus are combined to define a new subclasses defined in the open unit disk. In particular. We look into a convolution property, and we'll use the results to look into our task even more, we deduce the sufficient condition, coefficient estimates investigate related neighborhood results for the class $ \mathcal{S}^{\ell, \jmath}_q(\lambda) $ and some interesting convolution results are also pointed out.



    加载中


    [1] F. Jackson, On $q$-functions and a certain difference operator, Transactions of the Royal Society of Edinburgh, 46 (1909), 253–281. http://dx.doi.org/10.1017/S0080456800002751 doi: 10.1017/S0080456800002751
    [2] F. Jackson, On $q$-definite integrals, Pure Applied Mathematics, 41 (1910), 193–203.
    [3] M. Ismail, E. Merkes, D. Styer, A generalization of starlike functions, Complex Variables, Theory and Application: An International Journal, 14 (1990), 77–84. http://dx.doi.org/10.1080/17476939008814407 doi: 10.1080/17476939008814407
    [4] M. Naeem, S. Hussain, S. Khan, T. Mahmood, M. Darus, Z. Shareef, Janowski type $q$-convex and q-close-to-convex functions associated with $q$-conic domain, Mathematics, 8 (2020), 440. http://dx.doi.org/10.3390/math8030440 doi: 10.3390/math8030440
    [5] H. Srivastava, M. Tahir, B. Khan, Q. Ahmad, N. Khan, Some general classes of $q$-starlike functions associated with the Janowski functions, Symmetry, 11 (2019), 292. http://dx.doi.org/10.3390/sym11020292 doi: 10.3390/sym11020292
    [6] F. Alsarari, S. Alzahrani, Convolution properties of q-Janowski-type functions associated with $(x, y)$-symmetrical functions, Symmetry, 14 (2022), 1406. http://dx.doi.org/10.3390/sym14071406 doi: 10.3390/sym14071406
    [7] M. Govindaraj, S. Sivasubramanian, On a class of analytic functions related to conic domains involving q-calculus, Anal. Math., 43 (2017), 475–487. http://dx.doi.org/10.1007/s10476-017-0206-5 doi: 10.1007/s10476-017-0206-5
    [8] B. Khan, G. Liu, T. Shaba, S. Araci, N. Khan, M. Khan, Applications of $q$-derivative operator to the subclass of bi-univalent functions involving q-Chebyshev polynomials, J. Math., 2022 (2022), 8162182. http://dx.doi.org/10.1155/2022/8162182 doi: 10.1155/2022/8162182
    [9] H. Srivastava, Operators of basic (or $q$-) calculus and fractional $q$-calculus and their applications in geometric function theory of complex analysis, Iran. J. Sci. Technol. Trans. Sci., 44 (2020), 327–344. http://dx.doi.org/10.1007/s40995-019-00815-0 doi: 10.1007/s40995-019-00815-0
    [10] H. Srivastava, M. Arif, M. Raza, Convolution properties of meromorphically harmonic functions defined by a generalized convolution $q$-derivative operator, AIMS Mathematics, 6 (2021), 5869–5885. http://dx.doi.org/10.3934/math.2021347 doi: 10.3934/math.2021347
    [11] M. Raza, H. Srivastava, M. Arif, K. Ahmed, Coefficient estimates for a certain family of analytic functions involving a $q$-derivative operator, Ramanujan J., 55 (2021), 53–71. http://dx.doi.org/10.1007/s11139-020-00338-y doi: 10.1007/s11139-020-00338-y
    [12] M. Ul-Haq, M. Raza, M. Arif, Q. Khan, H. Tang, $q$-analogue of differential subordinations, Mathematics, 7 (2019), 724. http://dx.doi.org/10.3390/math7080724 doi: 10.3390/math7080724
    [13] P. Liczberski, J. Połubiński, On $(j, k)$-symmetrical functions, Math. Bohem., 120 (1995), 13–28. http://dx.doi.org/10.21136/MB.1995.125897 doi: 10.21136/MB.1995.125897
    [14] F. Alsarari, Certain subclass of Janowski functions associated with symmetrical functions, Ital. J. Pure Appl. Math., 46 (2021), 91–100.
    [15] P. Gochhayat, A. Prajapat, Geometric properties on $(j, k)$-symmetric functions related to starlike and convex function, Commun. Korean Math. Soc., 37 (2022), 455–472.
    [16] F. Al-Sarari, S. Latha, T. Bulboac$\check{a}$, On Janowski functions associated with $(n, m)$-symmetrical functions, J. Taibah Univ. Sci., 13 (2019), 972–978. http://dx.doi.org/10.1080/16583655.2019.1665487 doi: 10.1080/16583655.2019.1665487
    [17] F. Al-Sarari, S. Latha, B. Frasin, A note on starlike functions associated with symmetric points, Afr. Mat., 29 (2018), 945–953. http://dx.doi.org/10.1007/s13370-018-0593-1 doi: 10.1007/s13370-018-0593-1
    [18] K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan, 11 (1959), 72–75. http://dx.doi.org/10.2969/jmsj/01110072 doi: 10.2969/jmsj/01110072
    [19] A. Goodman, Univalent functions and nonanalytic curves, Proc. Am. Math. Soc., 8 (1957), 598–601. http://dx.doi.org/10.1090/S0002-9939-1957-0086879-9 doi: 10.1090/S0002-9939-1957-0086879-9
    [20] S. Ruscheweyh, Neighborhoods of univalent functions, Proc. Am. Math. Soc., 81 (1981), 521–527.
    [21] K. Padmanabhan, M. Ganesan, Convolution conditions for certain classes of analytic functions, Indian J. Pure Appl. Math., 15 (1984), 777–780.
    [22] H. Silverman, E. Silvia, D. Telage, Convolution conditions for convexity, starlikeness and spiral-likeness, Math. Z., 162 (1978), 125–130. http://dx.doi.org/10.1007/BF01215069 doi: 10.1007/BF01215069
  • Reader Comments
  • © 2023 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(1166) PDF downloads(73) Cited by(0)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog