• Overview of Chinese core journals
  • Chinese Science Citation Database(CSCD)
  • Chinese Scientific and Technological Paper and Citation Database (CSTPCD)
  • China National Knowledge Infrastructure(CNKI)
  • Chinese Science Abstracts Database(CSAD)
  • JST China
  • SCOPUS
LI Ming, ZHU Aoli. Hankel Determinants of the q-Starlike Function[J]. Journal of South China Normal University (Natural Science Edition), 2023, 55(6): 116-122. DOI: 10.6054/j.jscnun.2023085
Citation: LI Ming, ZHU Aoli. Hankel Determinants of the q-Starlike Function[J]. Journal of South China Normal University (Natural Science Edition), 2023, 55(6): 116-122. DOI: 10.6054/j.jscnun.2023085

Hankel Determinants of the q-Starlike Function

More Information
  • Received Date: July 19, 2022
  • Available Online: February 26, 2024
  • Based on the starlike function in classical geometric function theory, the class of q-starlike function which is related to q-derivative was studied in this paper. By applying Carathéodory-Toeplitz theorem, the coefficients of Carathéodory function were parameterized. With this contribution, the coefficients and its related Hankel determinants of q-starlike function were observed with the application of the relationship between classes of Carathéodory function and q-starlike function. The upper bounds of the coefficients and several Hankel determinants of q-starlike function are obtained in this paper.

  • [1]
    DUREN L P. Univalent functions[M]. New York: Springer, 1983.
    [2]
    KAC V, CHEUNG P. Quantum calculus[M]. New York: Springer, 2002.
    [3]
    ISMAIL E H M, MERKES E, STYER D. A generalization of starlike function[J]. Complex Varables, 1990, 14: 77-84.
    [4]
    VERMA S, KUMAR R, SOKÓL J. A conjecture on Marx-Strohhäcker type inclusion relation between q-convex and q-starlike functions[J]. Bulletin des Sciences Matéma-tiques, 2022, 174: 103088/1-10. doi: 10.1016/j.bulsci.2021.103088
    [5]
    SHABA T G, ARACI S, RO J S, et al. Coefficient inequali-ties of q-bi-univalent mappings associated with q-hyperbolic tangent function[J]. Fractal and Fractional, 2023, 7(9): 675/1-20. doi: 10.3390/fractalfract7090675
    [6]
    CANTOR G D. Power series with integral coefficients[J]. Bulletin of the American Mathematical Society, 1963, 69(4): 362-366.
    [7]
    POMMERENKE C. On the Hankel determinants of univalent functions[J]. Mathematika, 1967, 14: 108-112. doi: 10.1112/S002557930000807X
    [8]
    HAYMAN W K. On the second Hankel determinant of mean univalent functions[J]. Proceedings of London Mathematical Society, 1968, 3(18): 77-94.
    [9]
    JANTENG A, HALIM A S, DARUS M. Hankel determinant for starlike and convex functions[J]. International Journal of Mathematical Analysis, 2007, 1(13): 619-625.
    [10]
    CHO N E, KOWALCZYK B, KWON O S, et al. The bounds of some determinants for starlike functions of order alpha[J]. Bulletin of the Malaysian Mathematical Sciences Society, 2018, 41: 523-535. doi: 10.1007/s40840-017-0476-x
    [11]
    CHO N E, KOWALCZYK B, LECKO A. Sharp bounds of some coefficient functionals over the class of functions convex in the direction of the imaginary axis[J]. Bulletin of the Australian Mathematical Sociery, 2019, 100(1): 86-96. doi: 10.1017/S0004972718001429
    [12]
    KWON O S, SIM Y J. Sufficient conditions for Carathéo-dory functions and applications to univalent functions[J]. Mathematica Slovaca, 2019, 69(5): 1065-1076. doi: 10.1515/ms-2017-0290
    [13]
    LECKO A, SIM Y J, S'MIAROWSKA B. The fourth-order Hermitian Toeplitz determinant for convex functions[J]. Analysis and Mathematicla Physics, 2020, 10: 39/1-11. doi: 10.1007/s13324-020-00382-3
    [14]
    KOWALCZYK B, LECKO A. Second Hankel determinant of logarithmic coefficients of convex and starlike functions[J]. Bulletin of the Australian Mathematical Sociery, 2022, 105(3): 458-467. doi: 10.1017/S0004972721000836
    [15]
    郭栋, 汤获, 敖恩, 等. 从属于叶形区域的解析函数的Hankel行列式[J]. 数学的实践与认识, 2021, 51(9): 188-193.

    GUO D, TANG H, AO E, et al. Hankel determinants for analytic function subordinate to a leaf-like domain[J]. Mathematics in Practice and Theory, 2021, 51(9): 188-193.
    [16]
    JURY E I, MANSOUR M. Positivity and nonnegativity conditions of a quartic equation and related problems[J]. IEEE Transactions on Automatic Control, 1981, 26(2): 444-451. doi: 10.1109/TAC.1981.1102589
    [17]
    OHNO R, SUGAWA T. Coefficient estimates of analytic endomorphisms of the unit disk fixing a point with applications to concave functions[J]. Kyoto Journal of Mathematics, 2018, 58(2): 227-241.
    [18]
    FEI J, YEH C N, ZGID D, et al. Analytical continuation of matrix-valued functions: Carathéodory formalism[J]. Physical Review B, 2021, 104(16): 165111/1-10. doi: 10.1103/PhysRevB.104.165111
    [19]
    LI M, SUGAWA T. Schur parameters and the Carathéodory class[J]. Results in Mathematics, 2019, 74: 185/1-13. doi: 10.1007/s00025-019-1107-7
    [20]
    SIMON B. Orthogonal polynomials on the unit circle, part 1:Classical theory[M]. Providence, RI: American Mathematical Society, 2005.
    [21]
    TSUJI M. Potential theory in modern function theory[M]. Tokyo: Maruzen, 1959.
    [22]
    LIBERA J R, ZŁOTKIEWICZ J E. Early coefficients of the inverse of a regular convex function[J]. Proceedings of American Mathematical Society, 1982, 85(2): 225-230. doi: 10.1090/S0002-9939-1982-0652447-5
    [23]
    PROKHOROV V D, SZYNAL J. Inverse coeffcients for (α, β)-convex functions[J]. Annales Universitatis Mariae Curie-Sklodowska Sectio A, 1981, 35(15): 125-143.
  • Cited by

    Periodical cited type(1)

    1. 冀占江,刘海林. G-利普希茨跟踪性、G-等度连续和G-非游荡点集的研究. 华南师范大学学报(自然科学版). 2024(04): 111-115 .

    Other cited types(0)

Catalog

    Article views (100) PDF downloads (41) Cited by(1)

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return