Fourth Hankel and Toeplitz determinant estimates for certain analytic functions associated with Four Leaf function

• R. Rudrani ^[2] ; R. Bharavi Sharma ^[1] ; S. Sambasiva Rao ^[3]
  1. [1] Kakatiya University

     Kakatiya University

     India

     
  2. [2] Department Of Mathematics Government Degree College(Autonomous),Narsampet, Warangal, India
  3. [3] Department Of Sciences And Humanities Svs Group Of Institutions, Warangal, India

  Mostrar afiliaciones +
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 40, Nº 2, 2025, págs. 197-217
• Idioma: inglés
• DOI: 10.17398/2605-5686.40.2.197
• Enlaces
  • Texto completo
• Resumen

  • The objective of this paper is to establish initial coefficient inequalities, Upper bounds to the Hankel and Toeplitz determinants for certain normalized univalent functions defined on the open unit disk D in the complex plane related to the analytic function ϕ4L (z) = 1 + 5z/6 + z5/6 that maps the open unit disk in the complex plane onto the interior of four leaf shaped domain in the right half of the complex plane.

• Referencias bibliográficas
  • M.F. Ali, D.K. Thomas, A. Vasudevarao, Toeplitz determinants whose elements are the coefficients of analytic and Univalent functions, Bull....
  • M. Arif, L. Rani, M. Raza, P. Zaprawa, Fourth Hankel Determinant for the family of functions with bounded turning, Bull. Korean Math. Soc....
  • M. Arif, M. Raza, H. Tang, S. Hussain, H. Khan, Hankel determinant of order three for familiar subsets of analytic functions related with...
  • K.O. Babalola, On H3 (1) Hankel determinant for some classes of univalent functions, Inequality Theory and Applications 6 (2010), 1 – 7.
  • S. Gandhi, Radius estimates for three leaf function and convex combination of starlike functions, in “Mathematical Analysis I: Approximation...
  • K. Ganesh, R. Bharavi Sharma, K. Saroja, K. Yakaiah, Fourth Hankel and Toeplitz determinants for a subclass of analytic functions subordinate...
  • A.W. Goodman, “Univalent functions, Vol. I, Vol. II”, Mariner Publishing Co., Inc., Tampa, FL, 1983.
  • S. Gunasekar, B. Sudharsanan, M. Ibrahim, T. Bulboacǎ, Subclasses of analytic functions subordinated to the four-leaf function, Axioms 13...
  • W.K. Hayman, On the second Hankel determinant of mean univalent functions, Proc. London Math. Soc. (3) 18 (1968), 77 – 94.
  • G. Kaur, G. Singh, Fourth Hankel determinant for a new subclass of Bounded turning functions, Jnanabha 52 (1) (2022), 229 – 233.
  • M.G. Khan, B. Ahmad, J. Sokól, Z. Muhammad, W.K. Mashwani, R. Chinram, P. Petchkaew, Coefficient problems in a class of functions with bounded...
  • M.G. Khan, N.E. Cho, T.G. Shaba, B. Ahmad. W.K. Mashwani, Coefficient functionals for a class of bounded turning functions related to modified...
  • B. Kowalczyk, A. Lecko, The sharp bound of the third Hankel determinant for functions of bounded turning, Bol. Soc. Mat. Mex. (3) 27 (2021),...
  • B. Kowalczyk, A. Lecko, Y.J. Sim, The sharp bound for the Hankel determinant of the third kind for convex functions, Bull. Aust. Math. Soc....
  • B. Kowalczyk, A. Lecko, D.K. Thomas, The sharp bound of the third Hankel determinant for starlike functions, Forum Math. 34 (5) (2022), 1249...
  • R.J. Libera, E.J. Ziotkiewicz, Coefficient bounds for the inverse of a function with derivatives in P, Proc. Amer. Math. Soc. 87 (2) (1983),...
  • W. Ma, Generalized Zalcman conjecture for starlike and typically real functions, J. Math. Anal. Appl. 234 (1) (1999), 328 – 339. doi.org/10.1006/jmaa.1999.6378
  • W.C. Ma, D. Minda, A unified treatment of some special classes of univalent functions, in “Proceedings of the Conference on Complex Analysis...
  • S. Mandal, P.P. Roy, M.B. Ahmad, Hankel and Toeplitz determinants of logarithmic coefficients of inverse functions for certain classes of...
  • J.W. Noonan, D.K. Thomas, On the second Hankel determinant of areally mean p-valent functions, Tran. Amer. Math. Soc. 223 (1976), 337 – 346.
  • K.I. Noor, On the Hankel determinants of close-to-convex univalent functions, Internat. J. Math. Math. Sci. 3 (3) (1980), 477 – 481.
  • Ch. Pommerenke, On the coefficients and Hankel determinants of univalent functions, J. London Math. Soc. 41 (1966), 111 – 122.
  • Ch. Pommerenke, On the Hankel determinants of univalent functions, Mathematika 14 (1967), 108 – 112.
  • Ch. Pommerenke, “Univalent functions”, Studia Math./Math. Lehrbücher, Band XXV, Vandenhoeck & Ruprecht, Göttingen, 1975, 376 pp.
  • V. Radhika, S. Sivasubramanian, G. Murugusundaramoorthy, J.M. Jahangiri, Toeplitz matrices whose elements are the coefficients of functions...
  • V. Ravichandran, S. Verma, Bound for the fifth coefficient of certain starlike functions, C. R. Math. Acad. Sci. Paris 353 (2015), 505 – 510.
  • T.G. Shaba, S. Araci, B.O. Adebesin, Fekete-Szegö problem and second Hankel determinant for a subclass of bi-univalent functions sssociated...
  • K. Sharma, N.K. Jain, V. Ravichandran, Starlike functions associated with a cardioid, Afr. Mat. 27 (2016), 923 – 939.
  • H.M. Srivastava, Q.Z. Ahmad, N. Khan, B. Khan, Hankel and Toeplitz determinants for a subclass of q-starlike functions associated with a general...
  • H.M. Srivastava, G. Kaur, G. Singh, Estimates of the fourth Hankel determinant for a class of analytic functions with bounded turnings involving...
  • H.M. Srivastava, N. Khan, M.A. Bah, A. Alahmade, Ferdous M.O. Tawfiq, Z. Syed, Fourth order Hankel determinants for certain subclasses of...
  • P. Sunthrayuth, Y. Jawarneh, M. Naeem, N. Iqbal, J. Kafle, Some Sharp on coefficient estimate problems for four-leaf-type bounded turning...
  • D.K. Thomas, S.A. Halim, Toeplitz matrices whose elements are the coefficients of Starlike and Close-to-convex functions, Bull. Malays. Math....
  • S.P. Vijayalakshmi, T.V. Sudharsan, T. Bulboaca, Symmetric toeplitz determinants for classes defined by post quantum operators subordinated...
  • K. Yakaiah, R. Bharavi Sharma, Fourth Hankel and Toeplitz Determinants for a class of Analytic Univalent Functions subordinated to cos z,...
  • Zhang, Hai-Yan, and Huo Tang, Fourth Toeplitz determinants for starlike functions defined by using the sine function, J. Funct. Spaces 2021,...